Which male units will pass Pegasus Knight as an available class to their daughters?

Solution 1:

A father that has access to male-only classes (Fighter and Barbarian) will pass on a female-only class instead. A father with access to Fighter will pass on Pegasus Knight to their daughter and a father with access to Barbarian passes on Troubadour. The exception to this is Vaike, who for some reason, despite having access to both Fighter and Barbarian, gives Knight and Mercenary to daughters instead. Guess he has something against mounts?

So, Gaius, Donnel, and a male Avatar will pass on Pegasus Knight to a daughter. If you're looking just to pass on the Pegasus Knight skills, a number of male children can get those from their mother - though male child characters whose mothers don't have access to Pegasus Knight will never be able to acquire Pegasus Knight skills.

Source: http://serenesforest.net/fe13/children.html