Hairdressser: "What’s your background"

My hairdresser asked me this question to which I responded “Jewish”.

He goes “no no that’s not your background that’s your religion, where is your family from”

To which I responded “Poland” But obviously I wouldn’t call myself Polish

I asked him what his background was and he goes “yeah Greek”.

I felt so stupid what would you guys say to this. It annoys me that such a simple question is so hard to answer for a Jew and even harder for others to understand.