I often encounter phrases like this in anime & manga, but from what I understand they are quite common in real life too. A girl asks a boy "do you like/love me? no? so then you hate me?". To me this sounds very strange. In Russian, and I believe in English as well, saying "I don't love you" means just that, and doesn't at all imply hatred. Does it work differently in Japanese? Does 好きじゃない in this case really imply hatred/despise/antipathy? If that's the case, what's a better phrase to use to avoid hurting the other person's feelings?
Being passive-aggressive in complicated situations is part of their culture. If you ask someone if they loved you, they could simply answer no. If you, however, ask them if they hated you, you will rarely hear yes.
好きじゃない can imply that you hate the person, because 好き mostly means like, not love. There are several options how you can deal with the situation.
Your safest bet is "I like you as a friend."
This implies that you'd still like to remain friends. If that's not the case, you can just say sorry.
Saying sorry is the most useful phrase that can get you out of most situations in Japan. This way you won't even have to finish the sentence.
"Give me some time to think about it" already implies that you are going to say no, but the other person has more time to prepare him or herself for the final decision.
There's a fourth way, while I don't recommend using it, I've had Japanese people did this to me. You can say yes, go away on the first opportunity you get, and just ignore the person. This way you won't see the person getting hurt, but they will probably take it worse than a straight-up refusal.
Whichever option you take, you can make the other person feel a slightly better, and say that you are happy that they think so dearly of you.