Birth or Sun Signs are never on cusps, so without the year of birth, I can't tell if your BF is Libra for sure. It has to be one or the other. The Sun doesn't really move to each new zodiac sign on the 21st of the month, that's sort of an average. So look it up using his year of birth too, just to be sure. People exhibit traits of the sign next to them because usually their Mercury or Venus is close to the Sun but in the different sign. I just want to clear up this "born on a cusp" business first.
In all my years of practice in astrology, I only know two successful couples who stayed married and are the same Sun Sign. Both have Sun in Capricorn and are very serious. So I don't usually recommend being with your own Sun sign. In physics, there is a rule, "Like forces repel." So you are so much alike it can be as if you are with yourself. But the other planets matter too.
Libra is the marriage sign, they love to be in a relationship and often can work together too. It rules the marriage house. You tend to be stubborn or persistent, with Leo rising and a Taurus Moon. But Leos are strong and regal, and if he is Libra, he will appreciate that about you. Taurus Moon is sensual and romantic. You know what you want in life and have goals.
The Aries Moon can make him temperamental and a little immature. You always want to think you are right and are bossy. I don't know his rising sign. Your Leo or Fire sign rising goes well with his Fire sign moon though. I don't really have enough information to know why he is behaving as you say he is. Libras can be very patient if it's for someone or something they want. It's not a really selfish sign. So he must have other planetary placements which make him selfish or difficult. Taurus is a peaceful Moon, so I am not sure what makes you so angry. He gets over it faster because of the Aries moon.
I don't think it's worth it for anyone to stay in a relationship where they are deciding whether to let the other person throw tantrums or decide how to fight against each other. This situation sounds negative and I would just get out of it, astrology aside. None of the questions you asked were positive, it's all about tantrums and fights. I don't think either one of you is mature enough for a serious relationship right now. Try to talk it out, and see if it gets better. If not, move on.