chicktwins,
One of my stepdaughters spent a number of years as a vet tech, and remarked once on the emotional strain of putting an animal down. Shelly's a thoughtful young lady, and questioned the distinction between putting an animal down to avoid the suffering of illness or injury, and the arduous work when it was her employer's "turn" to euthanize the animals at the pound that could not be re-homed. The former, she had no question about, the latter was a challenge as to whether life confined to a pound is better than no life at all. She is perceptive and practical enough, as well, to recognize that the costs of maintaining an animal can be a factor in either case.
I'll digress for just a moment to interject that our last dog, Miss Maya, was a pound dog that Shelly could not make herself put down. She came to live here. A (mostly) shepherd mix. Not the smartest dog I ever knew, but as faithful and doting a companion as I ever had in a dog. Her liver gave out suddenly this past June. Shelly's younger sister got to blitzing her siblings, her mom, and me, with texts about the decision to have her put to rest. It descended at times into sniping, but it was about Maya, not me. A frustrated kid who just moved 700 miles away learning that the dog she grew up with was at her end. All understandable, to be expected, and tolerable . . . until we all got copied on a text with her questioning (not knowing that the deed was done at that point) if I wasn't taking the "easy" way out. Well, I'd been there cradling my sweet pal Maya's head as the vet and her tech saw to a dignified end to her life. Easy??? The gods smiled upon me such that I was able to hold my tongue. That's where Shelly stepped in. She was terse in her reply, without being sharp. What she laid out to her sister in that text brings me back to your point.
No one of good character kills any animal without having an honest purpose for doing so. That purpose might be to end or prevent the animal suffering. In the case of butchering, one may pause to reflect that the animal has been well-husbanded for its intended purpose. It's one's thoughts during that pause, however long or brief, that speaks to whether or not taking that life is right.
One of this year's batch of layer chicks, a White Wyandotte, developed a severely crossed beak. I watched her, and she actually thrived for quite a while. The biggest pullet in the coop. I have an idea that she rose in the pecking order because her pecks were actually pinches. But she started failing and quickly. I had to cull her.
Easy? No. Right? Yes.
From what you describe, it sounds like you're handling it right, outlining the reality of those two questions and their answers for your daughters.