There doesn’t seem to be a clear reason from what I can tell. However, he doesn’t like yellow and brown; that much is very clear from what I’m seeing online. I’ve never read “The Curious Incident of the Dog in the Night Time,” but it actually sounds like something I would love since I love detective fiction.
That said, I’m afraid to find the reasons because of spoilers. If I spoil it for myself, I will not read it, so what I’ve pulled together from the little snippets I’ve read is that Christopher hates yellow and brown because he thinks it’s a good thing to have reasons why you dislike something, but I can’t find those reasons. Not without potentially spoiling something, anyway.