Por seems to have a root meaning of "in the general location/area/place of" to me.

Por aquí - Around here (the general place of)
Una cosa por la otra - One thing for (in place of) another
Yo trabajo por él - I work for (in place of) him
5 por 5 = 25 - Think of five items, and now in the place of each of the five items, there are five items. 5 in the place of 5. Five in five places. 5 x 5 = 25

And then from there it changed a bit, but I feel like the heart is still there. It's definitely a stretch sometimes but

Por - because of, which is a little farther from the "in the place of meaning", but it still implies a close relationship.

Trabajo aquí por el dinero. I work here because of the money. The reason I work here is (abstractly) in the same place as money.

I dunno, just remember por = 'because of'.

Which then makes "por qué" make more since. It is literally "because of what".

Por qué tienes que irte?
Why do you have to leave?
Because of what do you have to leave?

So never say "por qué de" because that's more like "because of what of".

More examples taken from SpanishDict:

La contacté por correo.
I contacted her by mail.
(Notice how by in English means "next to" or "near" usually)

Viajé por Francia y España.
I traveled through France and Spain.
(Through = moving through an area)

Tengo que trabajar por ocho horas hoy.
I need to work for eight hours today.
(The working is occupying the same amount of space (in a temporal since of the meaning) as eight hours.)

Por ejemplo
For example
In the area of an example

Por favor
Please
In the area of a favor

Por supuesto
Of course
In the area of certainty

Por ciento
Percent In the area of 100

Por fin
Finally
In the area of the end