"Me neither" jars my ear, so I prefer "neither do [or whatever verb] I".
I can't speak Chinese > neither can I [rather than 'me neither]
I don't want to see that movie > neither do I [rather than 'me neither']
She isn't very intelligent > neither am I [rather than 'me neither']
Just a humorous observation here about
me too.
Comments at the end of a phone conversation:
A. I love you.
B. Me too.
Of course, B
means "I love you, too"; but technically B is saying, "I love me, too".