This topic came up at Christmas dinner with family. I had no luck coming up with a reason why they should care.

"Control" would not be a better argument with them. Everything is already controlled. What amazon, google, youtube, facebook, instagram, tiktok, netflix, spotify, recommend to you is all controlled. Various insurance (health, car, etc) is relatively controlled. Through an employeer you usually get health insurance. If you're self or un-employed they require, or did require, extensive health info before they would let you sign up.

And, I'm not entirely sure I disgree with that. Why should my premiums be higher because someone else wants to participate in risky behavior?

Like many here I go though lots of trouble to stay anon. VPNs, multiple unrelated browser profiles, multiple browsers, never use the same email address twice, differnt passwords, etc.... But I can't really think of a truely compelling reason to to give to my family why they should do anything similar.

I can mention things like the girl who's parents discovered she was pregnent when advertisers started sending her baby care ads. But, that's just not relevant to them.