Believing in magic does not mean that we have to have our minds so open that our brains fall out and roll around the floor.
There are limits to what magic can do in this physical world. One of the things that it cannot do is to change you into a mythical creature. One is human on this plane and remains human. Magic does not and cannot change your DNA.
I think it is important that one understand what magic is and what it can do before starting out as it saves a lot of misunderstandings and disappointments later.