Bad Dad stories are ones where the father, or more broadly the older male authority figure, is a bad man. This provides quick dramatic tension because where one expects the character to be reliable, well intentioned, benevolent or strong instead the Bad Dad is weak, destructive and possibly even evil.
Bad Dad stories need to have an actual father or close equivalent to a father in a role that is subverted to qualify. Stories where the authority figure who turns out to be bad but the role is such that either sex could have played it do not count.