Probably because people in your area often celebrate birthdays there. You would've seen it without the conversation as well. And it was one of probably 100 ads you and your wife saw over the days, you didn't notice the ones that were targeted badly.

You don't have to be lying about it, but consider that we often incorrectly detect patterns where none exist.

Two words, "lookalike modelling", or as FB calls it Lookalike Audiences:

https://www.facebook.com/business/help/164749007013531

Arcade Foobar want to draw in new customers, and so generate a lookalike audience based on data they have from existing customers. The modelling algo then compares data points for people who 'look like' their customers, and those people can then be targeted with a high probability that they will also be interested in the same thing.

This is a perfectly plausible explanation that doesn't require FB to be listening to you through your phone mic.

Complete nonsense. That you actually believe this instead of the much more plausible explanations are beyond me.

Why is it not plausible?

Because if Facebook was actually listening to your mic we would know it. They wouldn't be able to hide and it would be a massive scandal. It's simply too conspiratorial to take seriously when there is no evidence other than anecdotal stories like this.

Is this non-anecdotal enough for you? I'm tired of using the "conspiracy" label to shut down valid discussion.

https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=786909

https://www.cnet.com/news/samsungs-warning-our-smart-tvs-rec...

https://www.washingtonpost.com/news/the-switch/wp/2017/03/09...

You don't see any difference between Alexa (which wouldn't work without listening to everything) and Facebook secretly listening without your consent to use it for ad targeting? None of your links provide any evidence this would be the case, or even mention Facebook.