Speaking from the perspective of someone who would own the apartment being rented out:

If a couple with two kids want to rent a 2-bedder apartment (rather than a house) it suggests to me that they want to save money (ie: can't afford to rent a house) so that could make an owner wary.

Some people don't like having kids in their rentals - if its carpeted they may be worried about spew stains, if there are floorboards they may be concerned about scratches on the floor.

I tend to think that people who buy houses expect families to rent them and so expect the wear and tear associated, but people who rent out apartments are ideally looking for a single person with a high disposable income and no pets.

Not that I am saying any of the above is right or correct, but rather my summation of what the landlord might be telling the agent....