Beauty and the Beast was one of my favorite movies when I was a young teen and it came out. Now watching it as an adult, all I see is Stockholm Syndrome.
I see it differently, probably because of the way my parents explained it to me when I was little. Beast is the master of the castle, and has no one to curb him at all. When Belle snaps at him that she had run away because he had frightened her, he looks genuinely shocked, and does not have a come back. He is surprised that he scared her by yelling, because he is so convinced people are only scared of him because of the way he looks. Afterwards, he never raises his voice again. Not once. He roars at Gaston, but he never again yells.
My parents told me that if someone does not know that their behavior is wrong, you make an allowance that one time (unless it's physical violence). You give them a chance to apologize and make amends. Belle let him know his behavior was wrong, Beast apologized, made amends, and turned out to actually be a nice person who did not have good parents to teach him that it is not acceptable to yell when you do not get your way.
Disney's official explanation was that he was literally turning into a beast the longer he spent away from human contact, which they probably could have explained better - that his parents didn't teach him to behave in the first place, and lack of early teaching + curse = yelling and screaming tantrums.