Washington state used to allow hound hunting for cougar and bear. But pugetropolis passed an initiative to outlaw this very effective means of controlling these predators. So take your concerns up with the wise urbanites who dictate to the rest of the state on how to live our lives. The city of Aberdeen does not have the personnel nor training or equipment to take on big predators and WDFW is cash strapped. Their budget is supported by the hunting community purchases of licenses, ammo and gear and not the general tax payer. 
So if you like cats in your backyard thank Seattle if you don't want them in your back yard again thank Seattle.
And yes I have 3 children and they all have been raised to respect wildlife and learn how to live with it. I suggest you do the same.