@Alexis:
Hi! I like your profile picture. I'm an audio engineer so it always nice to meet other musicians.
I appreciate that you are not trying to be rude or argumentative. That's certainly not how I took it. This is exactly the sort of question that I posted hoping to be able to answer. I don't mind if someone understands the theory of evolution and then decides to disagree with it. It does bother me a little when someone thinks that I think their grandfather was a chimpanzee and discredits me because they misunderstand what I think, so I'm glad you're here to talk about this.
As T_Laurich points out, whether or not evolution is or is not the way that life developed, you seem to have some misconceptions about it.
Some of what I say here will borrowed from the book "The Greatest Show on Earth" by Richard Dawkins, who is a biologist and a notoriously abrasive Atheist. He has written some books attacking religion as a whole. "The Greatest Show on Earth" is not one of them, it just argues for evolution. Arguing for evolution may or may not be an attack on your specific brand of religion, so I won't recommend to everyone, but this book does an extraordinary job of explaining what evolution is and what it is not. If you are genuinely interested in understanding this theory fully, I highly recommend it. In fact, I'd be happy to send you my copy.
Firstly, the theory doesn't state that one species can give birth to an animal of a completely different species. Ultimately what we're looking at are extremely tiny differences from generation to generation that add up to quite a difference over time. For instance, think about your mother. You probably look rather like her when she were your age (your post says you're 15, so we will go with that). You probably look slightly less like your grandmother did at 15 than your mother did at 15, but your mother still looks rather like your grandmother did. Your ancestors 50 generations ago probably bear little to no resemblance to you or your immediate ancestors.
What does it matter whether they look like you or not though, right? They were still human.
The key lies in the timeline that we're dealing with. Species don't change much when we talk about them in the thousands of years. However, expand this to a million years (1000 thousands), and the animal we have at the beginning of this million years may could quite different from its descendant hundreds of thousands of generations down the line.
Again, what does it matter what they look like?
Well, there are certain physical attributes that can be helpful when it comes to survival.
I'm going to give you a hypothetical example. Let's make up an animal. It's a little like a horse and it's environment is the african savannah. Let's say the grass on the savannah isn't particularly good to eat and its best to graze on the leaves of trees. Two of these animals are grazing together. One has a very slightly longer neck than the other. While the one with the shorter neck can still reach the bottom leaves, it will not be able to reach some of the ones that the animal with the longer neck can reach. This means that animals in this scenario with longer necks will generally get more nutrients and will generally have a better chance of surviving to have children then those with shorter necks. This is known as natural selection. Animals who are best 'optimized' to their environment enjoy the best chance of survival - this is the survival of the fittest. A slightly higher number of short necked animals will die before they reach the age where they can reproduce. Since the long-necked ones have more children, the next generation has longer necks on average. Some with shorter necks still remain, but over a series of generations they will always be slightly disadvantaged and will eventually cease to be able to thrive as much as the long necked ones (mathematically, this is due to the law of large numbers). Each generation will successively favor longer necks until over the course of a HUGE timespan, we've gone from something that looks like a horse to something that looks rather like a giraffe.
Changes such as this aren't just hypothetical (although they are still theoretical; I will get to this in a moment). We can induce similar changes in animals over several generations, within the span of a human life. Since your family breeds dogs, maybe you will have heard of this:
A Russian researcher has left us an excellent example: He decided to breed foxes. He took a large number of wild foxes and tested them for how friendly they were to humans (typically foxes are skittish and can be aggressive). He took the most friendly among the group and separated them from the rest, then bred them. The result was that their children were generally friendlier than the group of foxes he had started with. He then took the friendliest among these foxes and bred them again, over and over. In each generation the friendliest foxes had the best chance of making it to the next round of breeding - that is, they had better odds of passing on their genes to the next generation. In this way he simulated how nature might favor some variations of the same species over the other (it's called artificial selection when it's induced by humans, your family very well might use it in their breeding practices). The difference between the foxes he started with and the resulting foxes is drastic enough that the foxes are naturally docile enough that the project is able to sell these foxes as pets, where their ancestors would have been highly aggressive.
One could make the argument that they simply trained them to a greater extent and that this is the cause of their friendliness, but they did the opposite experiment, breeding the most aggressive foxes of each batch and ended up with some very mean-tempered foxes.
Now, since you breed dogs, you'll also notice that while a beagle and a boston terrier are both dogs, they are rather different.
So animals might change from generation to generation, but how is it that we end up with different species? Again, the theory's answer to this is essentially time. It states that in the not too distant (anthropologically speaking) past, something similar may have been done with wolves: that the wolves which were most comfortable around people might have had an advantage to surviving to see the next generation. Perhaps those who scavenged from humans' camps had a higher survival rate than those who had to fend for themselves in the wild. Here you see the population split into two. The wolves who live off of human food scraps, etc. tend to survive better if they are more docile. The wild population has a better chance of surviving if they remain aggressive.
It is also important to remember that it isn't one single aspect of an animal changing over time, it is many of them. The wolves that are friendlier to humans might also have a better chance of getting scraps if they are cuter. This has no practical importance in terms of how they would survive in the wild, but once you introduce them to a new environment it very well could and two traits are changing simultaneously. In fact, there are too many possible variations of genetic traits to list here or pretty much anywhere, substantially more than two of them could mutate from generation to generation.
This is how one type of animal can become several distinctive types. If we started with a wolf-like creature in the last example, what we ended up with over ten of thousands of years are two very distinctly different types of animals: modern dogs and modern wolves. Eventually, the genetics diverge so drastically that the two species can no longer reproduce with one another and we now have two separate species instead of one.
Think of it in terms of languages. Most modern languages are young enough that we have pretty complete histories of where they come from. Many European languages come from Latin. I'm not a linguist so this will be highly oversimplified, but imagine at the fall of the roman empire, everyone speaks Latin. These many people are divided into separate groups. As the Middle Ages set in, roads fall into disrepair and travel is considered rather dangerous. People pretty much live and die wherever they were born. Over a series of generations in these tiny (by modern standards) communities, people change the way they pronounce words, the way they use grammar, cases, tenses, make up new words and expressions, all separate from the other communities that had once spoken the same language. In some places during the Middle Ages, the difference in language between people who had been isolated for so long from one another was such that eventually having a conversation with a person in a town within several miles was virtually impossible. Today we're left with distinct languages, many from the same source. Latin evolved into several modern languages with some similarities, but essentially mutually unintelligible - as though they had become different species from one another.
This is similar to biological evolution. The theory is a population becomes isolated and eventually evolves in a different way than the population it was separated from until they're so different that they no longer can be considered the same group.
Also important to note is that one trait can have an unintended effect on the other. In the fox experiment, the breeder bred only on the basis of which foxes were tamer. However, each successive generation got floppier ears, some started to develop spots. Genes are extremely complicated, its theorized that the gene for docility might have been sort of packaged with the gene for floppy ears so when you get one, you get both.
So the question, after experiments like the foxes (similar experiments have been done with multiple other animals and plants as well) is not, as you note, "can change occur over time?". It is "can it occur to the extent that we would eventually end up with a completely different species?"
My take is that if we can produce two drastically different types of foxes over as short a period as fifty years, its certainly not implausible that these changes amplified by the hundreds of thousands or millions might yield two animals that are not distinguishable as the same species.
I don't wanna load you up with evidence for evolution unless you ask for it since I said I was only going to answer direct questions and this post is already a little out of hand. I also don't want to discuss those on the forum until I hit T_Laurich's second post, which I meant to do tonight but it'll have to wait for another day.
When you say "it can't be recreated", that is to some extent true. We can't take an early primate and get to a human in the matter of a few years (or even a few thousand). We can induce some pretty drastic changes, though, as I've explained.
You mentioned that this might be it is classified a "theory". It certainly contributes to people using that title but even that wouldn't be enough to classify it as fact. The real reason is no one was there to watch it happen, so no matter how much proof we come up with, someone will always be able to say "yeah, but maybe not".
I don't think that the term 'theory' is inappropriate to describe evolution, but it can be misleading. The Oxford Dictionary lists several definitions for the word 'theory':
Def. 1: A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; a hypothesis that has been confirmed or established by observation or experiment and is propounded or accepted as accounting for the known facts; a statement of what are held to be the general laws, principles, or causes of something known or observed.
Def. 2: A hypothesis proposed as an explanation; hence, a mere hypothesis, speculation, conjecture; an idea or set of ideas about something; an individual view or notion.
People often use the word 'theory' to suggest that evolution fits under the second definition. It does not; It belongs under the first.
The reason it is considered a theory by scientists is because the standard of what is 'fact' in science is extremely high. While we are comfortable calling something we are 99% sure of a fact in daily conversation with one another, this is not the case in science. 2+2=4 is a fact. There is no other possible answer. Evolution has several alternative explanations, one is creationism. However, from a scientific standpoint evolution is the least complex. You may have heard of Occam's Razor. It is often misquoted as stating "the simplest explanation is always the correct one", while in actuality it means something closer to "the simplest solution is the one which we will deal with in the mean time, until it is either discredited or something else starts to seem more likely".
I imagine I wouldn't have too much difficulty convincing you that the Earth orbits around the Sun. Technically, this is classified as a theory (known as the heliocentric theory) in science. It is not the only possible explanation. The universe could move in such a bizarre fashion that it would merely seem as though this was the case. However, the heliocentric theory is simpler to the alternatives and according to Occam's razor is therefore the one with which we choose to deal.
Finally, you mention that - if true - evolution would be a matter of chance. I think that this is partially the case. If we go back to our African horse animals, our first two had slightly different neck lengths - one long and one short. There is a certain amount of chance involved in this. One happens to have a slightly longer neck, the way you might happen to be slightly taller than one of your classmates. What happens next is not chance. The longer-necked animal does not pass on its genes by chance, it passes them on because due to its physical attributes it survived more effectively than animals with shorter necks. The fact that we ultimately end up with giraffes isn't chance. It wouldn't have been equally probable that we end up with lizards - lizards would never have evolved in that environment because the attributes that make a lizard a lizard aren't useful there. Ultimately, the theory is that the environment guides the evolutionary process to its logical conclusion, which is never really a conclusion but just another step towards whatever will exist in the future.