I am probably the most privacy conscious person of my friends (not that I do a particularly good job of it), so I spent lots of time thinking about how to communicate about privacy in a way that is effective. [We're all mid-twenties, for context.] The main issue, I find, is that people just mostly don't care.
That being said, most of my friends do relate (and dislike) the loss of agency that comes with giving your brain to an algorithmic feed that decides what you eat. The narrative of "control your life and decisions" would be an effective piece of rhetoric, I think!
The other argument I've found really effective is one that convinced me after reading Edward Snowden's memoir Permanent Record. A sketch of the point:
Person 1: privacy matters. Person 2: I don't care about privacy, because I don't have anything to hide. Person 1: Historically, the folks who were hurt because of a lack of privacy weren't us (young professionals), but rather the civil rights movement in the 1960s and the Vietnam anti-war movement, etc. Privacy is about protecting those people who the government/institutions/etc already squash down.
It's an argument that comes from Permanent Record, pretty much, and I think for me it is the most compelling reason that I care about privacy! Not as much for myself (although that's nice), but mostly for the people that privacy protects who really need it.
In my experience, it goes over very well, as people can see that privacy isn't just about doomsday preppers not wanting anyone to know where they bury their gold, but rather about protecting those people who need/deserve/would benefit from protection!
P.S. I'd recommend reading Permanent Record. I was only 15 or so when all that stuff went down, and really didn't know anything about it except "Snowden good or bad idk," but the book is a fantastically interesting and well-written story. I think he's kinda awesome.