Stefano, It should be written like this: "I don't think so, either". This is most easily explained by saying that English is a crazy language. To begin, "Either" is being used as an adverb in this sentence, not a conjunction, so it doesn't mean one OR the other, and instead it's being used to mark a similarity (or agreement) between two objects in the sentence, in this case, you and the person you're speaking with. Conjunction and Choice both start with C, Adverb and Also both start with A, maybe you can remember it this way :) Conjugation either: "You can have either the blue shirt OR the black shirt, one or the other". Adverb either: "Sarah didn't go to the party, AND I didn't, either". I hope this helps :) Let me know if you have more questions!

When two things/feelings/opinions, etc., are the same and they don't contain a negative word (e.g., "not" or "don't") we compare them using "so" or "too" (e.g., "He likes pizza, and she does, too" or "He likes pizza, and so does she"). When two things are the same and they do contain a negative, we compare them using "neither/nor" or "either" (e.g., "He doesn't drive, and neither does she" or "He doesn't drive, and she doesn't, either"). Notice that when we use "neither" we reverse the auxiliary verb ("doesn't" becomes "does" in the second phrase). When we use "either," we keep the two negative auxiliary verbs (e.g., "John isn't Catholic, and Mary isn't, either").

'Either' in this expression is not used to express an alternative. This is a completely different use from in the construction 'either ..or'. In this expression, 'either' is used as the equivalent of 'neanche' in Italian. It is simply the negative of 'too'. A: I think it's difficult. B: I think so, too. (Anch'io) A: I don't think it's difficult. B: I don't think so, either. (Neanch'io) I hope that makes it clearer.