If you're tasked with mapping a subset of bit-states to negative numbers, it's intuitively obvious that there's already a state that yields 0 when you add 1 to it, as long as you wrap on overflow. With four bits that's 1111. That's a great representation of -1.
If you want to get 0 by adding 2, you'd have to start from 1110, and so on.
Just because the top bit can be used to identify a negative number when you use up half the states, doesn't mean it should be thought of as a logical flag. That's how you invent ones' compliment.
I think of ones' compliment as a logical encoding, and two's compliment as an arithmetic encoding, and it shows in how easy negation is in ones' compliment, and how easy arithmetic is in two's compliment.
The fact that everyone tries to teach them as if one is a precursor to the other is what's confusing.