Sometimes a person seems to be "protective" of us when they're actually being very controlling. They want to be your only source of information about things that you should, could, or shouldn't do in different circumstances. I'm with those who have said they didn't agree with her that it's dangerous to read for yourself.
However, since she didn't tell you what she meant by that so we can only guess what was meant, it's possible that she only meant that there's danger (of a sort) in reading for yourself because it's hard to be objective. You might want to ask her exactly what she meant if it's really bothering you. I don't believe reading for oneself is at all dangerous, but I do know that for me and many others I've seen commenting about it over the years, it's difficult to be objective about the readings we do for ourselves. If you like doing readings for yourself, then by all means, go ahead and do so.