[mesmark]

I agree with what Susan said. I just want to add that when you say "Me, too.", you are reiterating the same is true for me, but literally.

For me, if you say:

Quote thadajirajaras

A: I miss you.
B: Me too.

It sounds like B is saying "I miss me, too." B misses himself.

For me, it would only be natural to rephrase the sentence
A: I miss you.
B: I miss you, too.
(Like Susan said.)

The point is you are in agreement with what was said, not necessarily the idea. Does that make sense?

A: I want pizza.
B: Me, too. (I want pizza, too.)

A: I like Kenny.
B: Me, too. (I like Kenny, too.)

A: I love you.
B: Me, too. (I love me, too.)