I think it's absolutely 'normal' sure. Like Oowl said, we have a better "chemistry" with some than others (just as with other humans), that plus the more obvious reasons of a bird not being crazy about you.
I take care of all my birds equally and love them all no matter what, BUT yes I do have one that I'm extremely deeply (mutually) bonded with. Not only because I've had Robin my Red Bellied parrot for 20 years since he was a juvenile, but also because we have that special chemistry that I've never had quite as closely with any other pet before or ever...
Also commenting on Oowl's post, I agree about having a parrot pick you is best, BUT although I'm a long time parrot owner, I can say I've never done that. Consequently, it was hit or miss. Particular species I wanted either had to be shipped to me or came from closed aviaries (for health reasons) so I didn't pick them out in person. Griffin was a hit... Raven is, well, I hate to say a miss cause I do honestly love him, but he has always been clear that HE would not have chosen me, and he doesn't let me handle him. Others in the past same thing, hit or miss. You never know until you bring them home.
Robin my first parrot was suggested to me by the bird shop owner when I said I'd like a real parrot (had a tiel), and something a bit unusual (for back then). She said "I know exactly the bird for you". A certain Red Bellied parrot she had in mind. He was 3 months old and being returned to the store the next week by a family with kids who bought him and found quickly it wasn't going to work out. When I met Robin, I felt obligated at that point, and being a newbie I didn't really consider any of the larger birds around the store. Thank goodness it happened this way! Robin is truly my soulmate!