What do you think of this explanation of why subtracting a negative is the same as adding a positive?

The key observation is that if we confine ourselves to addition and subtraction (no multiplying), there is no difference between positive and negative numbers. Think of them as forces pulling in opposite directions. We tend to think of north and east as being positive and south and west as being negative. So think of the forces as being northwest and southeast, arbitrarily assigning positive to one and negative to the other.

For any equation involving addition and subtraction, we can reverse the signs of all the numbers and still have a true statement. Note that the + or – denoting addition or subtraction will remain. Part of the problem is the confusion of having these symbols to denote both operations and sign.

(+6) + (+3) = (+9) and (-6) + (-3) = (-9)
(+9) – (+3) = (+6) and (-9) – (-3) = (-6)
(-9) – (+3) = (-12) and (+9) – (-3) = (+12)

The equations on the right are obtained by reversing the signs of the equations on the left. If you accept the equations on the left then you must accept the ones on the right.