Two Pointers Logic

With pointers $left$ and $right$ on a sorted array: If $arr[left] + arr[right] < target$: move $left$ right. The sum is too small, and moving $left$ increases it.

If $arr[left] + arr[right] > target$: move $right$ left. The sum is too big, and moving $right$ decreases it. If they're equal: you found the answer.

Each step eliminates at least one element from consideration. After at most $n$ steps, you've checked all possibilities.