"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
Since your answer states that you dont like to drink a book... Not read