Good explanation of why it's optional in this case, although i'm not convinced that reason is the only reasonable antecedent of why. For example, the explanation why is a common usage,. Thus we say: You never know, which is why but you never know. That is why and goes on to explain:

There is a subtle but important difference between the use of that and which in a. As to why i do, i really don't know. (=but if you want to ask why i do, i don't know. ) i am going for sure. As to whether jane will go along too, you will have to ask her yourself. English is fun, as.

I don't know why, but it seems to me that bob would sound a bit strange if he said, why is it that you have to get going? in that situation. Why is used here as an interjection. According to merriam-webster: —used to express mild surprise, hesitation, approval, disapproval, or impatience