My boyfriend's insecurity / resentment is definitely showing through and now it almost seems like when we practice problems together it's like a competition for him to "prove" he's better.

This has nothing to do with CS and everything to do with your boyfriend needing to grow up.

When people use the term "toxic masculinity" THIS is exactly the kind of thing they're talking about.

How ridiculous would it sound if a woman resented her husband for making more money than her and then she was devoting energy to proving she was better than her husband in spite of that? How is this any less ridiculous? How is this healthy?

When I met my wife, I made more money than her. We moved for her career, and she currently makes more money than me (like 2x what I make). I'm starting a new job in a few weeks and I'll make more than her again. And you know what, it's never mattered. At all. It's all just "our money" anyway, not "hers" or "mine".

The fact that you're not married changes the dynamic a bit (since I assume your finances aren't unified and you still have "your" money vs "his" money), but it's still a really shitty attitude for him to have.