As a former landlord myself I actually preferred renting to a family. It's got to be the right kind of family, of course -- which makes the screening process so critical. In some cases, the property in question is more suitable for a family than for a single person or childless couple anyway (the more bedrooms, for example, the more conducive to a family).
But I would be seriously reluctant to rent to a family with a single parent unless I knew them well, since these are often unstable situations.
Most rental problems come from female head of household families - gangs, drugs, misbehavior. So your response is logical, but the law says you are wrong and the penalties are severe.