Neutrons are known to repel each other because of their strong force. When protons and neutrons become close to each other, there is a big possibility that they will exchange particles which means that they can be bonded together. There are times when strong forces will stop the repulsion from taking place, but the initial reaction of neutrons is that they will repel each other when they become too close.
This explains why neutrons are there. They are supposed to keep the balance within the atom. If only protons are available inside the nucleus, all of the protons will repel each other, and it may cause some issues to the atom. It may even be enough to make the atom break down.
Every thing we see around us is composed of atoms made of very small particles called protons, neutrons, and electrons. Neutrons, along with Protons, are in the center of the atom, and thus makes up the nucleus of the atom.
But since the Neutrons have no charge, they do not attract or repel. The protons have a positive charge, and the Electrons have a negative charge. These opposites make them attract each other. But since the Neutrons have no charge, they do not attract or repel.
The first time that neutrons are introduced to each other, their initial reaction is to become attracted to each other but the moment that they become too close, they will start to repel each other. The repelling will happen usually when they are 0.5 away. Take note that they are not electrically meant to be attracted or to repel each other because of their neutral charge.
The main reason why they are meant to repel more rather than attract each other is because of the known rule wherein like items will probably repel each other. This rule can be applied to neutrons too. This is the same when two protons are near each other, they will also repel each other or two electrons. Since they are the same, their tendency is to repel each other.