First, you are a very unpleasant person

You being wrong makes me unpleasant now. LOL. Okay. I'd say that fuckers who jump into to defend ignorant liberals in arnarchist forums are unpleasant, personally.

Second, that’s a weirdly specific definition of private property.

It's the definition that's been used by leftists since the advent of capitalism, and perhaps before. Yes, liberals' attempts to disarm our language by using to mean anything that's not owned by the state has done a number on your brain, making it sound "weird" to ignorant, propagandized fools. Can't argue with that.

Last, if I need to exploit other peoples labor to derive value to have private property, and we’re using violence to do it, then we just invented slavery again.

Yes, capitalism is wage slavery. Correct. It has somewhat different characteristics from chattel slavery (which capitalism still uses when convenient, such as in the U.S. prison-industrial complex), but slavery it is nonetheless.