Apple is pushing the privacy narrative because it's an area in which Google, and hence Android, cannot compete. Google/Android can't compete because the vast majority of Google's revenue comes from ads, which cannot work well with privacy.

Apple is spending lots of money to make privacy become important to the average smartphone user. It's spending that money not just to make itself look good, it's spending it to make Google/Android look bad, and thereby cause more users to switch to iPhone.