sounds like you have some real conflicts! i'm far from a therapist (watch it, there's always a *but* coming) but i've been in therapy for more years than you probably have been alive. at least i know some of the questions to ask and even a few of the (partial) answers.
no, it is not *normal* (whatever that is) to fear or shy away from therapy. this behavios is indicative of some underlying pboble.
is there something that you are afraid or reluctant to discuss with your therapist? this catagory can include suppressed memories.
does your therapist remind you of someone who perhaps hurt you or otherwise offended you in the past?
is your therapist going too quickly so that you are reluctant to go at that pace?
is this the right therapist for you? many therapists may be nice people, but not every therapist is for every patient. a therapist's first job is to gain rapport. this makes them come on as "nice". their second onvective is to find out what is troubling you and, finally, to use their skill, training, and experience to help you deal with these issues.
therapy is like pealing an onion: for every problem resolved (or seemingly resolved), there is another one that surfaces.
hope this helps. let us know how it's going.