Why do electrons repel

Yes, it's common question, and here is what I know so far.

1.like charges repel
2.opposite attract

but...

electron never do interact with each other in the sense that they never really touch because the charges keep them at a distance, is that correct?

now, i understand that electrons communicate via the electromagnetic force, and this is mediated by photons, correct?

as i understand, photons don't mind sharing space with other photons, so why in the case of charges, do they decide not to share space?

in conclusion. two electrons meet at a distance and start trowing photons at each other, but for some mysterious reason, some electrons stick together and other don't. WTF???

Richard Feynman, the world's best Physicist of the last half of the 20th Century is quoted to have said,"If you think you understand the quantum world, you don't understand the quantum world." This is because the quantum world is so strange to our little hypertrophied chimpanzee brains that it is truly non-understandable. And Richard Feynman won the Nobel prize in Physics for his work in the quantum realm.
But to answer your question, free electrons are singularities, which means they are essentially a naked negative charge floating through space, and they have no real size that anyone can discern. This means that you can get closer and closer to one, but you will never find anything like a surface. The laws of the Universe are set up such that bringing two electrons closer and closer together requires an input of more and more energy, with infinite energy required to force them to occupy the same space. Therefore it is simply impossible to bring two electrons together. If you ever find two free electrons in close proximity to each other, they will give off energy in order to get away from each other. Since all systems naturally proceed to their lowest energy state, that means that electrons repel each other.