-you say I haven't when someone asks you about if you have done something so it's about verbs
for example: have you traveled to Italy? you say "No,I haven't"
- you say I don't have when someone asks you if you have something.
for example: do you have some food? you say "No, I don't have"
so "I haven't" is for "Have you.." while " I don't have" is for "do you have.."