I am perpetually surprised how few people realize that only the first kind can be discussed rationally, while the second kind is at best a purely theoretical hypothesis.
So you start talking with them about realistic, scientifically achievable, immortality, and you end up answering arguments against mandatory immortality. WTH?
This is probably a topic that does not lend itself to rational discourse, kind of like politics or sex. Most people create this coping mechanism to enable them to deal with the prospect of their own demise, and end up unconsciously hostile to the idea of immortality.