The famous example I remember from growing up was a teen girl whose parents found out she was pregnant from a personalized (mailed) Target ad: https://www.forbes.com/sites/kashmirhill/2012/02/16/how-targ... . There seem to be some skepticism in later articles that this is actually how her parents found out, but only because she told them first. They could have found out from the ad.
https://www.liebertpub.com/doi/full/10.1089/big.2017.0074 is a more detailed study of how Facebook likes can out people. It looks like the "cloaking" solution that the authors propose actually makes the model more accurate. From the article "false-positive inferences are significantly easier to cloak than true-positive inferences".
If you're the only one who knows what ads you see, that might still be okay, but if a platform can make these kinds of inferences to show you ads, they can use the same data in other ways. At the very least, they might leak this information to other users by recommending people you may know, etc. You might also reveal what kind of personal ads you get if you ever browse the web someplace where other people can glance at your screen.
you wouldn't believe how irrelevant to me, the ads i get are.