Simple Harmonic Motion

A child jumping up and down is not an example of simple harmonic motion. I'm not going mad, right? Because I've just spent an hour arguing with my physics teacher who thinks that it is. No change in acceleration = no change in force = force isn't proportional to displacement

Perhaps if the child were jumping on a tightrope walk or a trampoline it would be more of a harmonic motion, because the negative amplitude must be the same as the positive?