I have a problem with the explanation of the particles は and が.
The problem comes up in season 3, “Things that you hate” chapter 7, here is the link: http://www.textfugu.com/season-3/hate/5-7/

Until then I thought I understood the usages of these two, but then two example sentences destroyed that Illusion.

First There is this part:
Q. いぬ が すき ですか？
Do you like dogs?

A. はい、いぬ は すき です。
Yes, I like dogs / Yes, as for dogs, I like them

with an explanation why at first が is being used and then, in the answer it’s は.
It is a nice explanation, works for me.

But then, nearly at the end of the site where the の particle is being explained:

Q.　わたしのくるまはすきですか？

A.　No, I hate your car. Translation →

いいえ、あなたのくるまがきらいです

Why? In this example it’s the other way around?
If following the same pattern and explanation as above we should introduce the car with が:
わたしのくるまがすきですか？
and then specify something about the already introduced car with は:
いいえ、あなたのくるまはきらいです

Can someone explain this?