These two questions are at the root of this conundrum, but you're not being completely accurate.
What exactly is your justification for regarding your right to privacy in your communication with your loved ones is more important than the right of the police to fight child abuse?
I believe most people would not agree with this exact proposition, but with a different one: that once the police is given the power to fight child abuse, which can only be given by allowing them to access private communications of anyone suspect of being involved in such crime, then there will be abuse of power and they will use that access to also fight other crimes or even for political gain, as tends to happen in authoritarian states.
I would absolutely be willing to forego my right to privacy under certain circumstances given that there were strong enough guardrails in place to prevent abuse in the future if that would allow child abuse and other hideous crimes to be prevented - it would be immoral to not do so. However, as most other people in tech, I have enough knowledge to understand that it would not be possible at all to prevent abuse with current technology - once the power exists at all to break into communications, anyone with enough motivation and resources available will be able to do it, not just the intended receipients of such power, unfortunately.
If you really want people on the other side of the debate to understand you, you need to stop being so simplistic - there are very good justifications for their positions if you remove the practical limitations of being able to stop abuse - which they do not understand, and I suspect a lot of people in tech even also fail to comprehend.
I would even go as far as to say that future technology may change this: it may be possible to have completely abuse-proof technologies in the future which, if it existed, would make me change my position on this matter.
For example, something that uses blockchain technology to make it cryptographically impossible for the police to access someone's communications without having a warrant?? And making that warrant only usable by the police if it was also approved by a number of different, independent groups, including groups advocating for privacy (something like a "smart contract" could do this?)??
You can say these are stupid ideas, and I would probably agree... but my point is that this may not be impossible, and perhaps people who are really concerned about privacy while also having an understanding of why the police may need this sort of power should be actually trying to find ways to do this properly instea d of just keeping repeating the mantra that no, this is impossible and we'll have to live with child abuse , terrorism etc. forever?!