In the sentence you are asking about, you should not use "too" or "either." Instead say, "He likes it, but I don't." Summary: positive + positive: Use "too." "He likes to dance. I like to dance too." negative + negative: Use "either." "He doesn't like to dance. I don't like to dance either." positive + negative: Don't use "too" or "either". "He likes to dance. I don't. negative + positive: Don't use "too" or "either." "He doesn't like to dance. I do." You can often combine two sentences into one: He likes to dance, and I do too. He doesn't like to dance, and I don't like to dance either. He likes to dance, but I don't. He doesn't like to dance, but I do. There are other ways of expressing the same thought, such as by saying, "Me too," "I do too," or "So do I"; "Me either," "Me neither," or "Neither do I."

"too" can not be used here. "too" should be used in positive sentence; "either" should be used in negative sentence.

"too" would not be used for the second sentence either. You could use it in an affirming sentence, for example: Person 1: "I like books" person 2: "I do too!"