Depends on where and what type of bug.
Bug in the house (like the bleepin' ants that have moved in here) yes, kill it. Then flush it.
Outdoors and just minding it's own business? Leave it alone.
Housefly that's been sitting on the poopy diaper garbage bag because it's 90 degrees out and we only have garbage pick up twice a month
? Kill it. Please.
Cutworm they find in my garden? Kill it. Same with the slugs.
Spiders around our porch? Leave them be, they eat flies.
I've never seen or heard of my kids killing bugs just to be cruel (think ant + magnifying glass) , they mostly just leave them be, with the exception of the slugs and cutworms, they actually hunt around in the garden to find and get rid of those. But it's not to be cruel, it's simply because those bugs destroy the garden that we've worked so hard on.