Have you also come across this strange opinion that Catholics and Christians are two separate and different religions?
What do you answer then?
I know that when I was a little kid (around 7-8 years old) I was an evangelical at the time, and I kept telling my Catholic neighbor friend who was maybe 5-6 that he wasn't Christian. But I had no theological basis for that, I was just going purely off the name. My childhood logic was "if they don't use the name Christian then they're not Christian."
As I got older I never held an opinion one way or another. My town overall was very unreligious and Catholics only made up maybe 15% of the population, they just weren't on my radar and my church community never talked about them like others tend to.
But if I had to venture a guess, I think it stems from the protestant inclination to come up with their own subjective definitions for the faith. What it means to be Christian, what it means to follow Jesus, everything. So, many of these groups simply state that to be Christian you have to accept Jesus into your heart as your personal Lord and Savior and believe (and only believe) what the bible says. Don't believe anything else (the irony, given that once a week a man stands up in front of everyone and tells them what to believe). Since Catholics don't fall within those terms, we're not Christians in their eyes.
Not that it comes up much for me, but if and when someone does ask if I'm a Christian I tell them I am, like
@HTacianas says, and if they ask where I go to Church I tell them whatever parish I'm registered at. I've yet to have someone push back on me though.