I don't believe it's unethical to breed bearded dragons provided that you've done your research, you treat your dragons right, give them the best husbandry, and your motives are good. To me, a wild animal, one who shouldn't be kept captive, is one who is never truly domesticated, one who always has some element of "wild" to their nature, and one who's needs can't truly be met in their entirety in captivity. Wolves, for instance, would fall into this category as would many zoo animals. Beardies, on the other hand, can thrive in captivity and many appear to enjoy the stimulation that comes with life with humans. It takes a specific set of requirements to fully meet their environmental and care needs, but as long as you're willing to put forth the effort to make sure a dragon gets what it needs, there's nothing unethical about keeping them. The dragon gets stimulation while also benefiting from the safety of captivity - nothing trying to eat them, no bad weather to get through, no daily struggle to find enough food for survival.
That being said, unfortunately many don't put forth this effort and many dragons are kept as ornamental pets in enclosures too small for any living thing to spend their lives in. It would be unethical for someone who keeps their dragons in that manner to breed, because in that instance, yes, the dragon would be better off in the wild. Sure they're safe and fed, but they can't meet their natural needs/instincts for exercise, activity, exploration, and general stimulation.
There is also the question of what will happen to the babies you breed? Even if you get a high quality male and a high quality female and have them in ideal enclosures under ideal husbandry conditions, are you willing to screen the people who buy the babies from you and educate them, or would you sell them to whoever replied to your ad because you need the money and space as the babies start to grow?
Basically the question comes down to: are you making the lives of the animals better for them, or not?
Ultimately though, since it is your dad's house I can understand not breeding while you're living there. As far as your female dragon goes, perhaps you could outline to him the ways her life will be good with you. She'll (hopefully) have a large tank with naturalistic conditions, and then also have lots of time out of that tank to interact with you and explore the world around her. She'll have a healthy balanced diet and be free from the threat of predators. Perhaps after your dad sees the relationship between you and your dragon he'll come to change his mind on the concept of dragons in captivity.
