thanks Elizabeth, that actually what I meant, just wrote a wrong example.

Anastasia, that's not correct. If somebody says "I don't like apples" we do NOT say "I don't like either". That is wrong. We say "I don't like THEM either". "I don't like either" has a completely different meaning to "I don't like THEM either". They do not mean the same thing.

Thank you @Anastasia! It is very useful!

Actually, there are some other examples as well. 'Cause @bluebottle explained you the use of either..... or and neither....nor But there are also such examples as Pete doesn't like apples. and you say: I don't like them either (so, basically either = too, but instead of too in the negative sentence we use either) the other example is Pete doesn't like apples. Neither do I. (Neither do I = I don't like either, but as we know there can't be 2 negative forms in one sentence, we use neither) you can't say "I don't like neither".

Thank you for the tip! So, I can use "either" when the sentence is "positive". And I can use "neither" when it's negative. Basically?