Your question is biased because you assume FB / Google / OEM manufacturers and whoknowswhoelse are not listening in on private conversations. A lot of people think they are. It is unwise to discount their suspicions
In short, you can't. People want to believe what they want to believe. Maybe if you have someone receptive you can explain the absurd number of correlations advertisers can make from your profile, and the fact that a guess only has to be right once for it to see like Facebook is listening to you while advertisers make tens or hundreds of guesses every day. No one wants to hear this explanation though, so I wouldn't expect to convince anyone. :)
Buy a burner phone with cash in a different city that you live in. Install Facebook. Start a Netflix binge session show that is purely in Chinese or Japanese. Do nothing else then open a url with a lot of ads.
You can try to use some common sense. The risk of a security researcher finding out about it, or of a whistleblower coming out is too high. Something like that would not pass a risk-benefit analysis in any stretch of the imagination, specially for a company that already collects huge amounts of data from their users.
I don't think this is something Facebook would be able to come back from.
It actually seems easier to prove how to do this. I might actually hack together an app that listens in on conversations and transcribes it to profile a user. And then demonstrate how hard or easy it is.
That's weird. Even with VPN, different locations and different computers, I get pretty much the same result sets: lots of media sites with articles debunking it, the eff weighing in, some people documenting how they tried it and what they found etc. You get facebook.com a lot in the top 10?
