Military have a bad image among rescue groups and breeders for that very reason. They are known to dump pets when they move or are deployed, then get a new one when they return from deployment or are settled at next post. They receive extra scrutiny from breeders and rescues, while some just will not place an animal with military period.
As for what parents or grandparents did with surplus or deformed animals, that was a different time. Today, there are numerous rescues and shelters who would take those critters off your hands and either give them a home or give them a more humane ending than drowning, and the terror the poor animal must feel during that.