My TV keeps switching on the AVR by itself (or the AVR changes inputs on its own). What's happening?

That is HDMI-CEC doing its job, just not the job you wanted. CEC is the control channel that lets devices switch each other on, change inputs and share a remote. Useful when it behaves, maddening when devices from different brands interpret it differently.

Two facts explain most of the misery. First, every manufacturer names it differently in the menus (Anynet+, Bravia Sync, Simplink, Viera Link, and so on), so people switch it on in one box without realising it exists in another. Second, CEC is a loosely enforced standard: a streaming stick that wakes and announces itself at 2 am can pull the TV and AVR up with it. Nobody at the standards body watched a film at your house.

You have three sane options.

Embrace it fully and let the TV drive. One remote turns everything on, switches inputs, controls volume. This works well when the devices are recent and mostly the same brand, and it is what most of our clients settle on once the misbehaving device is identified.

Selectively disable it on the device that misbehaves. In our experience the usual suspect is the streaming stick or a games console, whichever likes to wake up and announce itself. Turn CEC off on that one device and leave the rest talking.

Disable it entirely and use one universal remote or a control app to manage sources. More manual, completely predictable. Some households prefer predictable.

There is no correct setting, only the combination that suits your devices. What I would not do is randomly toggle it on three boxes at once, because then you cannot tell which change fixed what.

One important note: some TVs require CEC on for ARC or eARC audio return to function. If you disable CEC on the TV and lose sound from the AVR, that is why. Check both settings together, and if the two conflict, the fix is usually moving the source to the AVR directly.

If you tell us the exact TV, AVR and source models, we can point at the likely offender rather than guessing.