Can you provide any additional detail about that? I can’t tell if you’re referring to FB mining the contents of the messages, or the app doing unscrupulous things in the background.
The NSA says they only monitor communication metadata. But that's already a lot of information. Let's imagine a scenario where FB can't read your messages, so it doesn't know what you talk about. But if you talk to people who are mostly Trump critics according to their Facebook activity, Facebook can probably categorize you as a liberal. If you added a new friend of the appropriate gender for dating, and your communication intensifies, Facebook can probably guess what's going on. If it intensified and goes quiet some evenings (predominantly weekend evenings), well, guess who's seeing each other (each guess come with probability percentages).
The latter. I don't have specific examples in mind, just that if you do not trust a company's data collection policies, the collection capabilities of an installed program are much greater than when viewed through a web browser. See [1] for an example from a few of years ago.
When you think about it, it's kind of alarming that FB, Messenger, WhatsApp and Instagram are all owned by the same company. I can't even imagine the amount of data they have about us.
