I think a lot of y'all 'unbelievers' are taking the word "soul mate" way more literally than the 'believers' are.
Do I believe that for every person, there is a perfect match, and that their souls are eternally bound to each other? No, I don't, because as was already pointed out after death we will become like angels and there will be no marrying and such.
However, I absolutely believe that God has a perfect match for you to run your race with in this life. No, that doesn't mean that they are 100% alike or compatible or whatever. But their characters compliment each other's, and complete what the other lacks. That said, I also believe there are "Pauls" in this world, people who don't need a running mate in life. There aren't too many, but they are out there. On the other hand, there are also people out there who simply NEED to be married. I know at least one out of each of those two categories.
But even if you do find your soul mate, or rather, running mate, there will absolutely be ups and downs, fights, arguments, because even if that is the person God chose for you, you must remember that the both of you are still human.
I don't really think God leaves us to our own devices about anything. Just like he arranges events that will lead us to a certain door, I believe that God has a person out there (for most of us) who he has in mind for you. The trick is waiting on the Lord and making the right choices.