When fishing for Chinook salmon you are allowed to keep 2 jack salmon (salmon under 24 inches) per day as long as they are hatchery fish as evidence by the heald scar on the adipose fin. Since jack salmon are sexually immature and not considered as breeding fish, why does it matter if the jack is a hatchery fish or a wild fish? It is not a breeder anyway, so why not allow the keeping of wild jack salmon?
That's an interesting question - why do jack Chinook salmon get protection similar to what the adult fish get. Part of the reason is that they actually are sexually mature fish. Jacks are males that return to freshwater to spawn after spending only one year in the ocean and they do spawn. As a side note, there are some "jills" or sexually mature females that return each year that have spent only one year in the ocean. But the number of jills in any year is very, very low; typically less than 10 fish in a run of 80,000 total fish. Because the jacks are sexually mature they are important in the life cycle of salmon. In years of low Chinook returns when there are fewer female fish on the spawning grounds, it's good to have more males present to ensure the males can find the female fish and the eggs of each naturally spawning female are fertilized. Also, competition among the 1-ocean, 2-ocean and 3-ocean males to spawn with an individual female is important for maintaining the fitness of the populations. When the salmon populations have recovered to fishable levels, harvest of both jack and adult wild salmon can be allowed.
A correction on your interpretation of the daily limits is important so you can keep as many fish as the rules allow you to. For the Snake, Salmon, Little Salmon and South Fork Clearwater rivers the limit isn't 2 jacks per day but rather it is 4 Chinook salmon but not more than 2 may be adult fish. Under that definition of the limit an angler could catch and keep 4 jacks as their daily limit, or they could keep 3 jacks and 1 adult or 2 jacks and 2 adults. If you are fishing and have caught and kept 3 jacks, you can continue to fish for the fourth fish and keep that one whether it is a jack or an adult fish (assuming that the adipose fin has been clipped). If the first two fish you catch and keep are both adult fish, you cannot fish any more that day since you have achieved the adult limit. The reason for writing the rule that way is to provide more flexibility so anglers have greater opportunity to harvest fish. It is impossible for us to forecast how many jacks might return each year. If there are a lot of jacks we won't need as many for brood stock in our hatcheries so more harvest can be allowed. If there are not a lot the limits are still flexible to allow anglers to catch and harvest adult fish.