They are necessary to prevent the massive weight of the roof from pushing the walls. The benefit of having flying buttresses as opposed to traditional buttresses is that it lets much more light go through the windows. So you can have a higher and larger nave, with larger windows that receive more light.
The key to understanding this architectural choice is that cathedrals are meant to be seen from the inside and from the front, mostly.
Funny enough I think this was the common view when they were introduced as well. They were a necessary kludge to get certain interior features and through age and context they've become appreciated for their own sake.
