Here's an interesting question: When beginning a PhD, how much do you agree with your supervisor's theories about a certain topic, and does it change over the course of your research?
For example, say you were doing a PhD in a field where there were two big theoretical perspectives, and you'd thought about both but were quite happy on your side of the fence - but could see your supervisor waving cheerfully from the other. Would you see this as a useful learning experience - i.e. good to have a different set of academic influences, and making it important to really argue your point well to someone who would accept it less readily - or more as a non-ideal choice of PhD supervisor?
What are the downsides?