In a redox reaction, why does an element's oxidation number increase

If the element is oxidized, then it's oxidation number would increase.

Let's say we have the following reaction.

2H2O - - > O2 + 2H2

To the left, the oxidation number of O is - 2, as it is bonded to two H, which is always H+. To the right, we have O2, and all gases have a oxidation number of 0 (zero). We say that O has been oxidized.