The way Threads is implemented and is working is illegal in the EU, so Meta decided not to launch it in the EU until they figure out how to circumvent the laws.
I think the history of that is that Meta at the last minute decided that they couldn't launch Threads in the EU and that that sealed the faith of Threads leading to its now increasingly obvious failure in the market. It looks like a poorly planned and executed rush job by Meta that is now failing.
The reason the BBC is ditching Threads is because it has no traction worth talking about and because they are a European company and a European launch of Threads seems to be not happening. Mastodon is apparently good enough that they are not giving up on that one for now. Probably also really cheap for them to support it as they can self-host it. And given how critical they are of Musk, they need an alternative to X even if they still have to use it.
It's more than that: Meta is also in hot water because of handling of user data, behavior advertising, and using data from its seemingly separate apps across Facebook for tracking and advertising.
Threads runs afoul of many provisions in Digital Markets Act and possibly GDPR, too.