As an adverb, either is used at the end of a negative sentence in place of too and also.
- He said he didn’t like me and his wife said she didn’t either.
- “I can’t spell very well.” “I can’t either.” Or “Me, either.”
As an adverb, neither is used to introduce a negative statement to add to the one that has just been made.
- “I don’t like my father.” “Neither do I.”
- “I have never won the lottery.” “Neither have we.”