The opposition to chat control is really missing the point: chat control does not break encryption, the law is about mandating client-side scanning, not weakening cryptography so law enforcement can break it more easily or introducing backdoors. If you say "don't break encryption", they will just respond that this will not break encryption, which is true, but also completely irrelevant.

What we should be advocating instead is the freedom of doing whatever we want with our computing devices, which include rejecting the sort of crap companies and various government like to impose on ourselves.

Yes, it doesn't "break" encryption, it just defeats it.

The client-side scanning means that some amount of your communication will be uploaded in clear text to the government. And unless the government keeps it completely secure (spoiler: they won't) this will leak. Therefore it defeats the point of the encrypted channel.

So sure, it isn't as bad as just removing encryption from these apps. But it is very similar to giving the government a backdoor key to all messages. Maybe you see it as slightly better because only the messages flagged by the automated scanning are made vulnerable or maybe you see it as slightly worse because previously you would need both the backdoor key and access to the original messages and now all of the data you want is in a single location.

But the point is that this significantly weakens the security properties that these E2EE messengers provide if implemented.