Well people have this belief that people are born with feelings towards things without any previous knowledge of their existence. So, if that is indeed the truth, then it is possible for someone to be born with the feelings against sex.
Just to be pedantic, and not actually address the whole of this post, people can actually be born asexual. For example a male may have no sex drive. Then when he takes up muscle-building sports or activities, this may boost his testosterone levels, which in turn may boost his sexuality to the point he now is interested in other people sexually, when he wasn't interested in people sexually before.
Conversely a sick male who was previously sexual may lose all interest in sex if his testosterone levels drop too far.