We can reply So / Neither / Nor
+ auxiliary +I
when we have something in common with someone:
'I like this cheesecake.'
'So do I.'
Sometimes we want to make it clear that we are different:
'I thought the film was quite boring.'
'Oh, I didn't. I really liked it.'
In this case, the second speaker has given a short answer with an auxiliary I didn't
and a short explanation.
I don't like this music.'
'Really? I do. I've always been into heavy metal.'