Why does switching doors in the Monty Hall Problem increase odds: 2 doors, 50-50

Question

I have read through around 10 articles and webpages on this problem, and still don’t understand. I’ve run simulations and yes, switching does get you better odds, but why?

In: Mathematics

Answer 1

With 100 doors the odd for a single door is 0.01,
the host removes 98 wrong doors,
you have still a door with an 0.01 odd.

Only in 1 out of 100 cases your door is the right door
but in 99 cases your door was and is the wrong one.

Taking out 98 wrong doors after your choice did not change the quality of the first choice.