I think that's a great question OP.
I'd agree with that
It is Distributivity (and the fact that multiplication is distributive) that dictates that (-1 x -1) must equal 1.
Distributivity means that if you multiply a whole load of numbers by Y and then add them up, you get the same answer as if you added them all up first and then multiplied that sum by Y i.e. 2x(1+2+3+4) = (2x1)+(2x2)+(2x3)+(2x4)
And now the proof (Requires that you believe/understand that (-1 x 1) = -1
)
Consider the equation -1 x (1 + -1 + 1) = ?
First you add up the bits in the brackets and you get (1 + -1 + 1) = 1
Then you multiply by -1 to get the answer (-1 x 1) = -1
Now try employing distributivity to do it the other way
You would get:
(-1 x 1) + (-1 x -1) + (-1 x 1) = ?
See you have a (-1 x -1) bit in the middle. Assuming (-1 x -1) = -1 you would get the following:
-1 + -1 + -1 = -3
Which is different to the answer for the way the equation was previously arranged.
The only way it will work is if (-1 x -1) = 1, as below, thus fulfilling the requirement that multiplication is Distributive.
-1 + 1 + -1 = -1