Question

why do charges attract or repel ?​

Answer 1

Two electrons will tend to repel each other because both have a negative electrical charge. Two protons will also tend to repel each other because they both have a positive charge. On the other hand, electrons and protons will be attracted to each other because of their unlike charges.
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Answer 2

This question has very deep origins, up to our basic understanding of the nature of matter.

The best way to understand the answer of this question intuitively is to recollect what is a charge. Now, what is a charge?

Our modern understanding of this question is that a Charge is an intrinsic property of matter, due to which it interacts with the electromagnetic field.

When the concept of charge was realized (about 1800 s), people realised that there was some unique property of matter, due to which it started attracting/repelling other objects, when rubbed with certain objects. This was later studied in detail, and later as physics developed further, Quantum Mechanics was formulated, we have a quite reliable notion for what "would" be the reason (most probably) why the forces act as they do. (* Most probably because we don't know for sure. We can't probe at such minute distances to see for ourselves.)

Our current understanding of why the forces act, as they should is influenced by the Exchange Field Theory which was postulated by Yukawa in 1960 s. Yukawa explained that every force (fundamental) propagates due to exchange of certain particles, between the two bodies. These certain particles are called the force carriers of that particular fundamental force.