Cliff, come on, you are a lawyer. You know that these things are fluent.
I mean, I totally trust Apple when they say that they are only using it to check iCloud uploads (and frankly, it is indeed a more privacy-oriented solution than server-side checking), and when they say that they use NCMEC databases. However, why should I trust it to remain this way? Client-side scanning sets a dangerous precedent — once the system is in place, it is trivial to extend it to other purposes. What if Tim has an accident in a year or so and a new Apple CEO is more open to making a deal with totalitarian regimes in exchange for market access and tax benefits? Or if they decide to extend the scanning to your private pictures that are not even stored on the cloud (which would be a trivial thing once the framework is in place). Or even more, scan all all the image data that goes through the APIs? Or what if a new governing body comes to power that redefines what "child endangerment" mean (there was already an example of Hungarian law that makes "gay propaganda" a criminal offense)? These are the real issues. It's not what we have now, it's what becomes easily possible in the future.
For now, I am not affected by these changes. I live in Europe and even though there is a lot of pressure to make surveillance more prevalent, European politicians are generally much more privacy-oriented and generally sane than their colleagues in the USA. But they are also massively incompetent and I worry that these developments will nudge our legislation in the wrong direction.
And let's not even start with the philosophical and moral part of the issue, as this kind of technology comes very close to violating the presumption of innocence.