Your question is impossible to answer because you have not provided any context - you have not told us what was said before 彼は好きじゃない. It could mean the following:
- I don't like him (but I do like someone else).
In this case the は particle serves to compare 彼 with someone else. The fact that 私 is the person speaking is hidden.
- He doesn't like it.
Here, what 'it' is is known from the context of the surrounding conversation. 'It' could be apples, you, me, anything.
Just a suggestion, Japanese is highly contextual. You have to know what was said before in order to know the 'real correct' translation of something. Using a tool like Tatoeba which gives you single sentences with other people's translations based on what they think is the surrounding context will cause you confusion.
