Some players here just want to play a lot of different opponents and don't care for rematches. Some just signed on to play a couple of blitz games or one rapid game when they have a little free time and don't have time for a rematch. Some have a favorite trap or trick they rely on and don't want a rematch after you have seen it. Don't get upset when your opponent doesn't agree to a rematch, just play someone else.
If you don't like opponents who harass or insult you you, leave chat turned off.
Thanks for the advice about using time well, I'm not old enough to have learned that lesson yet 
You are not entitled to a rematch. Your opponent is not entitled to a rematch. Refusing a rematch is not unsportsmanlike because there could a variety of reasons someone declines, whether it be that they don’t want to play or have some other business to attend to.
There is a huge difference between "fair play," and "ppl playing how/when OP wants them to." Violating fair play - cheating - isn't even similar to what is being described here. You might argue that the behavior you are describing is a little rude, but honestly, even that is just a matter of opinion.
There are so many similar troll threads to this one, that I wonder why it has been opened in the first place.
So being polite and giving your oponent the chance to show his true strenght is not a good thing? Then, let's forget about rematches since no one would grant you or you would look like a beggar asking for one. Who is the troll then, huh?
There is a huge difference between "fair play," and "ppl playing how/when OP wants them to." Violating fair play - cheating - isn't even similar to what is being described here. You might argue that the behavior you are describing is a little rude, but honestly, even that is just a matter of opinion.
+1
[Moderator - Removed_GC]
In conclusion, it will be better if they remove the rematch option as long as you are mislead by others to play after winning with others, only to find yourself in the stupid position to be ignored when you want rematches!
By the way, to all the people commenting here against my idea, you don't show that you're really better than another player after just a game. You only show that you speculated a mistake! That's all!
1. Don't remove the rematch option, because some people do accept. Not all, but some. It's nice if you lose to someone, think you could've done better, ask to play them again, and they accept. It is not mandatory, and it's just an option. Why get rid of it if it doesn't give you exactly what you want 100% of the time? It's an option that some people enjoy, and by existing it doesn't insult you.
2. It's a game. You're not proving that your better than anyone. You're simply having fun.
Nice!
<<Refusing/Ignoring Rematches.>>
Come on now, do you think it's compulsory to accept rematches or do you think people should be sent to prison for immorality if they don't accept them? People have all sorts of reasons not to accept them, which don't involve just wanting to wind you up. Better to fit in with other people's wishes.
Refusing rematches is not poor sportsmanship.
Creating threads to whine about your sense of entitlement to expect rematches, on the other hand...
Bad ideas generate other bad ideas. The OP's notion is getting the attention it deserves: rejection.
The old "hit and run strategy". It may seem cowardish, but at least it has proven to be efficient...