Be very careful, I find a lot of people put the importance of romantic relationships above and beyond the important of anything else. We've always been taught as children, teenagers, adults, through the media, TV, schools and books that LOVE is the ultimate source of happiness, and because we're taught that we believe it, but in reality it is not the case. Love is a good thing and it is a source of happiness but it's not the only one. You need to learn to realize that, realize that you don't need your boyfriend to be happy, and if he's not trustworthy and he's doing these things, than he's not worth you.
I suppose it's a self-confidence thing as well in a way, in your entire conversation you've been constantly rationalizing his behavior, as if you're in the bad and he's in the good. But you have to stand up for yourself and realize that in this scenario, you're in the good and you don't need him to be happy. Even if you don't break up, showing a bit of self-confidence and strength will make him listen this time, without him just ignoring you. People respect someone who is able to stand up for themselves.
Good luck!