For some people, it might be because of time wasted. I mean, we're all different. We all have different reactions. Yet it isn't all about that, it isn't that simple of an answer. Why remain bitter when you can be happy? Because we human beings aren't robots who can simply control our emotions at will. Emotions are beyond logic. Even if you WANT to not be bitter, it's not as easy as turning on a switch in your head and saying "Don't be bitter, me!"
Now, my own reasons... it's difficult not to look back and think about the good times... and how they're all over now. For me, that's the part that gets me depressed. I become angered that we were forced apart by some irreconcilable issue, that things can never be the same again. And that extends over to not being able to interact with that person, being bitter because... well, we just didn't click for one reason or another. Really, a breakup in itself is a complicated thing. There can be so many different reasons to be bitter because it all depends on the context or what happened. So it isn't something that can be neatly explained in one package. It's a different answer for each individual situation. For me, it's a feeling of betrayal. I take my relationships very seriously, and when they falter in this way... I feel the other person has betrayed me, they've betrayed a promise we made to each other to be together. Is it logical? No. But that's how feelings work.
It's better to be bitter towards them as well because... some of us, we don't have that sort of restraint. It's a shield for me, to prevent us from getting back together and repeating the same exact mistakes. I've absolutely been burned by this and second chances.
I don't feel like it's a waste of time, but also, I'm honestly not happy either that I had to go through more shit in my life. It just happened. So that reasoning doesn't apply to everyone.
But I'll put things in a basic blanket sort of way to try to answer the question: If you had something good happening to you, something you were really invested in... and then it was suddenly taken away, would you not be super pissed off and bitter? Especially at the person you perceived as giving it to you no longer doing so? Absolutely.