Overstocking is never a good thing to do in any permanent tank no matter which way you look at it
What happens is fish have much less room to swim in,
territorial wars/bullying will break out especially if you have many mixed species
injuries occurs and
these lead to stress
when fish are stressed this leads to susceptibility to diseases
diseases lead to deaths more often than not.
One other factor in overstocked tanks, water conditions will become difficult to control due to the amount of waste the overstocked fishes will produce. Will then need more water changes will have to take place to control water parameters, guppy2002 has basically already listed these points about dirty water already.
If that does not convince them then ask them about this last thing, fish deaths means having to spend more money on getting more fish, money for meds to treat the stressed/injured fish, more money on de-chlorinator and more money for the higher water bill due to all the water changes needed.
That should do the trick hopefully.