The reason is stability or we can call it neutrality.
Matter wants to possess neutral state. A negative charge wants to give away its electrons to become neutral therefore it attracts positive charge towards it. On the other hand, a positive charge requires electrons to become neutral, that is why it moves towards negative charge.
The same concept explains the repelling particles, if we place a negatively charged particle near another negatively charged particle, these two particles contributes towards unstable environment of the two particles. This situation can be better explained by human activity analogy (consider a person who is feeling the heat of the summer, what will provide him more comfort, an air conditioned room or direct heat under the sun. I hope, everyone has the answer for this). Similarly, the two particles possessing same charge become more unstable near each other, therefore to gain stability they try to repel each other and move away from each other's affinity.