Today's Grammar Point

Try to find the mistake in this conversation, then go down the page to check.

A:     I've never been to Okinawa.
B:     Me too.
A:     Do you want to go there?
B:     Yes, but I want to go in summer.
A:     Me too.

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NOTE {but not the mistake}: In natural English it is not necessary to say "there".
"Do you want to go?" is OK.     So we can use:

"Do you want to?" - maybe this is a little too easy and casual but native speakers do say it.
"Do you want to go?" - natural
"Do you want to go there?" - natural
"Do you want to go to Okinawa?" - unnatural, please don't repeat the same noun so soon

Anyway, could you find the mistake in the conversation?

A:     I've never been to Okinawa.

B:     Me too. --> Me neither.  /  I haven't either. 

A:     Do you want to go there?

B:     Yes, but I want to go in summer.

A:     Me too. 

"Me too" is for two positive verbs (simple verbs with no ..n't)
A:    I like dogs.
B:    Me too.  /  I like dogs, too.

A:    I can ski.
B:    Me too.

"neither / .... n't either" is for negative verbs (verb + n't)
A:    I don't like dogs.
B:    Me neither.    /    I don't either.    /    I don't like dogs either.

A:    I can't ski.
B:    Me neither.   /      I can't either.