Okay, I'm gonna start off with a dictionary definition of proud: having, proceeding from, or showing a high opinion of one's own dignity, importance, or superiority.
Don't you just hate it when you come across someone who thinks they're so much better than you? It's so infuriating. You just want to wipe that smile of smug satisfaction off their grinning gob and let them eat a bit of humble pie. Well, I guess that makes it kinda clear why Paul didn't want people to connect love with proud. It causes anger and resentment. But even when it doesn't, it still has pretty bad repercusions. I'm sure you've heard the saying 'pride comes before a fall'. The reason is, pride puffs you up so much that you can't see where you're putting your feet, and then wham, you're on your face. So be careful about priding yourself in your relationships too much. That's a bit of a sneaky trap. You start to think 'hey, I'm doing pretty good at this whole loving thing', get a bit proud, and that's when you start seeing people as not being people.
Maybe you think I'm overdramatising a bit. Well, let's look at it this way. A little bit of pride in a relationship, you might think is a good thing. It means you want to keep it going. But this links in with the whole boasting thing. If you start looking at your relationship in terms of what it provides, that can never lead to good stuff. A relationship is about what you can give, not what you can get. And that is the very essence of love.
Remember: God made you special, and he loves you very much.