Videos that you downloaded from other people aren't yours. You might own a copy, but that's no different from any other system of distribution. The difference between p2p and standard distribution is that the owner loses control.
However, a centralized near-monopoly grants itself certain power over the spread of information: if everyone uses it and it bans your video, the video may essentially be unknown—despite your intent. That is losing control, both for you personally and for us as a society: we lose control of our videos by using one big centralized platform, which lets it hide them from us.
An interpretation of PeerTube’s slogan could be that switching to it you take control of your videos by making them less liable to become hidden due to e.g. censorship—but also in that publishing something useful on it you by extension also bring viewers into the ecosystem and thus help society as a whole take that control back by reducing its dependency on a centralized source.
"The people who can destroy a thing, they control it." - Dune
Google owns it.
With peertube and the like, maybe you don't own it, but at least Google doesn't either.
Then why are they advertising with the slogan "take back control"???
It doesn't say "take control away from Youtube and Google", it says take back control of your videos. p2p is the ultimate destruction of control, that's the entire point of it. Saying that peertube gives you control is like saying that playing a slot machine gives you ROI.
With p2p, control is transferred away from Google to you and anyone else that chooses to host it. This is reasonable justification for using "take back control" to me.
I guess you'd also object to GPL being described as "more free" than MIT.
the owner retains control of distributing their voice without a major platform getting in the way
If you want to get off a platform, you can do that with a website. You don't need to give up editorial and retractive control forever (which you must do in order to use p2p, which is why this headline is so wrong) just to step off a platform.
(putting aside the fact that peertube is NOT A P2P distribution platform[1])
P2P is not different from any kind of distribution mechanism for digital content: the moment you put your content online, you've lost a good chunk of control over it since anyone can now download it a re-upload it elsewhere. This is automatic for p2p, but it also happen all the time on youtube, (or worse, porn tubes).
There is no way around it so far, and DRMs have largely failed preventing that. So any content creator must know this at this point: once you've published something online, you cannot reliably unpublish it.
Now, when you go through a centralized platform you also lose one more part of control: not only you cannot unpublish it, but you also cannot guarantee that it will remain published. This is the part of control you can get back by using peertube or other federated or distributed streaming system.