A magnet can exert a force on a moving charged particle, but it cannot change the particle's kinetic energy. Why not?

If a force doesn't really move a body in the path of force it doesn't do any work on the body. The magnetic force is always at 90 degree to the direction of the velocity, so this does not work. It just pushes the moving charge

F = q * v x B and F is perpendicular to both v and B, meaning there is no magnetic force displacement along the direction of motion.