Take it with a Grain of Salt
If you go digging in ANY disney movie there are going to be severe issues with messages they are trying to portray to children, however one movie is not going to affect how your children see the world. Nature vs nurture debate, which is important because sometimes disney likes to have odd messages, it is important to remember that if you raise your children correctly, any relatively odd messages will not hurt them. Beauty and the Beast (originally called Belle et la Bete) is a fairytale writing in 1771 which is actually very interesting to look up, however this is what disney based this movie off of therefore some of the themes are INCREDIBLY outdated. Also it is disney who likes to convince us that most women are evil so take it for what it is. As a kid's movie it is difficult to debate when we are reading too deep into things, some people have issues with the relationship between Belle and the Beast saying it is abusive, I think this is the point where people are reading too much into it, if this is the only movie your child watches, this could potentially be a serious problem, but I'm gathering your child is watching more movies than this, I do not think it is an issue we need to really freak out about. I mean Twilight has a much more horrifying message to children and few people ever freak out about that. But I'd also like to point out that this movie does have some good to it as well, I mean Gaston is the villain in the movie and he is trying to kill the beast for no justifiable reason other than he's the beast, and also when the beast is kind it also shows you cannot judge someone by how they look, they made him violent and aggressive I personally believe to showcase his frustration with what has befallen him and his human emotions, not to showcase an abusive relationship. That is solely personal opinion there, due to the fact that if you try and think in someone else's shoes, you can sometimes see such fascinating things. It's based on your personal opinions of the movie, but it will not damage your child if they see this movie.