Two Sum Sorted - Why It Works

Why does two pointers find the answer? Suppose the answer is at indices $i$ and $j$ with $i < j$. Initially, $left \leq i$ and $right \geq j$.

Every time you move $left$ right, it's because the current sum is too small. Since the array is sorted, the correct $left$ index must be further right.

So you never skip past $i$. Similarly, you never skip past $j$ when moving $right$ left. Eventually, $left = i$ and $right = j$.