So first it's client-side scanning for CSAM. Not without some nobility. But the problem is once you wedge open that door it's technically possible to do it for other things and so you become compelled to.
It'll move from just CSAM to stopping and tracking "propaganda" as deemed by them which will be narrow-ish at first (anything pro-Russia, RT links, etc) but gradually expand over time to anything outside the mainstream branded as extremist (and guess what, privacy advocates will definitely fall within that label). And once that's in place the private stake-holders, copyright holders will come knocking, they'll say rightly so "hey you have the capability right now, we demand you implement client-side scanning to detect copyright violations" and then that will be ordered by a court, further enshrined by a law and oh look now you can no longer send political thought that the ruling regime disagrees with, can no longer surf the high seas, and so on and so forth. Congratulations and please enjoy living in the "garden" of Europe.