When I say, "I don't like milk." Should the person respond "me either" meaning, I don't like milk either? If they respond "me neither" isn't that a double negative?

Question

When I say, "I don't like milk."  Should the person respond "me either" meaning, I don't like milk either?  If they respond "me neither" isn't that a double negative?

Thanks and I'm sorry.  I'm sure I didn't type that question correctly.

Jen · Answer

No, they would say me neither. It's not a double negative (because the only negative word is neither).

E.G. · Answer

I think the grammatically correct answer should really be: "neither do I"