Why is subtracting an expression similar to distributing -1? explain.

Take the expression 2x - (x - 3).  We know we can multiply everything by 1 and not change it; we know that if a variable does not have a coefficient with it, we can write a 1 beside it.  That means we can write our expression as
2x - 1(x - 3).  This helps us see the distributive property applies here:
2x - 1x - 1(-3)
2x - 1x - -3
2x - 1x + 3
1x + 3 = x + 3