Why do like poles of a magnet repel each other?

Like poles repel because their magnetic fields align in the same direction, raising magnetic energy, so the system pushes apart to lower energy.

Field lines from a north pole point outward; from another north they also point outward. Superposing two like-directed fields makes a high-energy, high-pressure region between the poles. Maxwell’s stress explains a net outward force. On the microscopic level, electron magnetic moments and currents oppose overlap due to both field energy and quantum exchange effects, yielding repulsion. Opposite poles reduce energy by linking field lines, so they attract.