Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.

2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.

In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.

2 - (2 - 2) = 2 + ((-2) + 2) = 2

2-(2-2)

But you broke the rule of left-associativity there. You can go right to left provided you keep each number with the sign to it's left (and you didn't do that when you separated the first 2 in brackets from it's minus sign).