My family is not Jewish, we’re messianic. But they call themselves Jews. How do I explain to them why it’s not okay?

The way I explain my religion is that we are Christians who have a loosely similar lifestyle to Jews. I don’t tell people I’m a “Jew for Jesus”, because that’s just not true. We are not ethnically Jewish and not a single person in my family has gone through the conversion process. But my family tells people they are Jewish and quite frankly it’s embarrassing. I seem to be the only person who understands we are not Jewish. I need a concise way to explain to them why they need to stop, so I figure who better to ask for help than the Jewish community.