If someone wants to build and train their own model that assigns a binary gender based on pictures that's their own choice, and because of that freedom they can't force google to do it for them.

Right, it's just that usually the concept with goods and services is that you're paying someone else to do it for you because you either can't or don't want to.

If I'm the author of the tool, I can impose whatever I want, no? It's not like people have a God-given right to have Google tag photos with genders for them.

So the best argument to do is the fact that you have a legal right to?

The argument in this case is that the potential for misuse outweighs the potential benefits.