This could be a Teaching English but it also could be a living in Taiwan question.
If you ask someone “Would you like me to make an appointment for you?”
" Would you like to go to…"
I often get a response. " I’m not going "
Is the proper response one of these…
No, thank you.
No, I don’t want to go
No.
But, “I’m not going” seems a little inappropriate and a little rudish.
I’m imagining the omitted part of your questions being “You should see a therapist. Would you like me to make an appointment for you?” and you’ve been asking these questions three-quarters of the way through any argument (minor or major) with your significant other for the past thirteen months. They are sick of the suggestion and don’t want to go, full stop. When they say “I’m not going” they mean “I’m not going, I will not be going, stop asking.”
If it’s another situation, 2 is what I’d choose most of the time.