Question

When a bar magnet is cut into two pieces why they repel?

Answer 1

This is so because when we cut a magnet into pieces then each piece acts as a single magnet. That is why like poles repel each other.
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Answer 2

So when we cut a magnet, nothing happens to the alignment of the net magnetic moment of the domains. We say that north pole is the place where magnetic field lines come out or diverge and the south pole is where the field lines go in or converge. So when we cut the magnet, there will be 4 places where field lines converge and diverge. The first half will form a magnet with it’s own north and south pole and similarly the second half becomes an independent magnet too.