First: you’ve done good, raising a kid that asks for your permission first.
Second: realize that this comes from peer pressure, them wanting a space away from parental supervision. If you truly want to make your kids savvy about the Internet, you need to assume they will eventually encounter seedy places, run into assholes, and be exposed to things like bullying.
Have a conversation: you will encounter these things. Your friends may be into them. But they can have bad effects and here is how you avoid it and how to deal if it happens to you. Talk about keeping private information private.
Be open and non-judgemental. You want them to feel safe coming to you for advice.
Be truthful and stay credible. Keep up with what’s out there, but don’t just buy into the latest Tiktok scare.
Talk to your kids about stuff they found that was cool or scary.
Embarrass them by using memes incorrectly.
Setting up a mastodon instance may be cool at first, but their friends are going to think it’s lame with the supervision. You could still do it for a number of other reasons, but it won’t prepare them for the ugly Internet.
Source: me, a parent.
It’s not a matter of software choice, in my opinion. It’s the network effect. Everybody is on Facebook.
Despite its falling out of favor of the younger generation, it still has massive inertia. There’s also the issue of (I think) the overall weariness of being on social media. The halcyon days of that is over; it has become a utility at best.
I think part of the reason I enjoy the fediverse is that it reminds me of the old Internet: loosely connected, federated but independent. We had irc for chat, usenet, and mailing lists. We had like half a dozen IM platforms and tons of bulletin boards.
With that in mind, the solution may be to just let the fediverse evolve: let people find the media that works for them, whether they are into photography, music, politics, whatever. Use the software that makes sense. You don’t have to declare a victor.
The real threat isn’t Facebook: it’s centralization and censorship. The more distributed and heterogenous your ecosystem is, the safer you will be.