I'm not sure which country you're from, but many EU countries do have private health insurance. The Netherlands, for example, has a system of subsidized private insurance, and a mandate that everyone buy a policy.
(If Americans are thinking, "huh, that sounds like Obamacare / the ACA marketplace!" then you're right.)
(If Americans are thinking, "huh, that sounds like Obamacare / the ACA marketplace!" then you're right.)