Well, this certainly is a blunt topic.
Here are my thoughts on why I say it is sinful.
Masturbation is essentially an imitation of sex. A Christian punk band called Lust Control says it well in a song called "The Big M". "Masturbation is artificial sex". By masturbating, you are, effectively, having sex, only without another person involved.
The lack of a partner also causes issues. When an individual achieves orgasm, several chemicals are released in the brain. Among these are one where, in that moment, essentially your brain takes a snapshot of that moment in time. It is forever glued into your mind. Achieving orgasm enough times and it would get jumbled around and lost in your head like any other memory might, but it is still an interesting distinct memory formation. The other chemical that I think is important is one which causes you to bond with your partner. I'd honestly go as far as to say this is intended by God to be for the spiritual aspect of being one flesh with your spouse. If you lack a partner, then you do not have someone to bond to during that moment. This, coupled with the whole memory formation thing can be problematic. I'm sure many who have struggled with pornography and masturbation will know what I'm talking about here. If you try stopping this behavior, your mind will draw on these images implanted on your brain when you become aroused. This can, in turn, lead to a relapse or sexual dreams and so on.
I'm not sure that I described that very well. Hopefully that made sense. The information about the chemicals comes from a book called Porn Nation by Michael Leahy.
My last big reason for thinking that it is sinful is simply that it is addictive behavior. It can often take over a part of a person's character, giving them a sort of secret life as a masturbator and a regular person. This behavior sometimes snowballs and is often where weird behaviors such as exhibitionism come from. I really don't think that anything that is addictive can be considered anything but sinful. I refer specifically to things that are universally addictive rather than something that simply can BE addictive, such as chocolate or video games.
Now, I do think there are legitimate reasons for someone to masturbate, though I think these are rare. For instance, if I were married, and 2 years into the married my wife was injured in some awful way that required the end of a sex life, I think it would be acceptable to turn to masturbation. The whole "spouse away on business" thing I hear sometimes is a little silly though, as I think the idea of waiting to see each other would result in much more passionate and, perhaps in its own way, a little bit more "romantic" because of the anticipation of waiting to be reunited would come to a close.
Lastly, I think that masturbation would always be a lesser evil to committing a sexual act with someone else outside of marriage. I can't truly envision a scenario where that would actually come up, but I just thought I'd share that.
Obviously this is all simply my opinion, but I thought I'd share. Sorry for being a little blunt, but I think that's the best way to discuss such topics.