"I hate reading books."
が vs は is the end-all-be-all biggest struggle of Japanese. I have asked so many native speakers by now, and their answers boil down to "whatever feels right". Don't feel bad for having trouble.
That being said, when you're using this particular structure, 「×」が(好き/きらい)です... you always use が. Never は. Unfortunately I can only provide you with a similar answer (it just feels wrong to say は). Perhaps someone else could help explain.
It greatly depends on context, saying「本を読むのはきらいです。」you're stating that the conversation topic is "reading books" (lit: As for reading books, (I) hate (it)). For example, here you can use は when talking about different hobbies, and want to say something in particular about reading books. On the other hand, with「本を読むのがきらいです。」you'd be identifying that reading books is what you hate indeed by using が, which would be used when asked something like "What do yo hate?", so you answer that, among all possibilities, "Reading books is what I hate".
Resources with more examples: http://www.guidetojapanese.org/learn/complete/topic_particles http://www.guidetojapanese.org/learn/complete/unknown
Like said below, in the case of like/dislike it's something like a set phrase structure:
This structure is needed, cause 好き/嫌い are na-adjectives, so a literal translation of the example sentence would be: Speaking of myself, the reading of books is disliked.
So the subject of the sentence (thus が) is the act of reading. So these kind of sentences are more similar to sentences like "The dog is big" where the adjective is used as a predicate. The はが-pattern is encountered often in Japanese grammar, e.g. "Americans are intelligent." may be rendered as アメリカ人は頭がいい/悪いです。"Speaking of American people, the head is good (=intelligent)/bad (=stupid)."