Do you kill bugs and insects that fly into your house or do you catch and release them?

Both.  Yes does make me feel like a murderer. 

Bugs are insects.

Entomology
an insect of a large order distinguished by having mouth-parts that are modified for piercing and sucking.

It is difficult to catch them and many are harmful, so I usually have to kill them. I can usually capture spiders, though.

Mostly catch and release. Mosquitoes that come in my house are executed and I don't feel a bit bad about it. 

i just scared them away with repeller
https://www.amazon.com/LEOFFY-Ultrasonic-Mosquitoes-Non-toxic-Extremely/dp/B07BZBJY5Y/ref=sr_1_4?ie=UTF8&qid=1528135302&sr=8-4&keywords=insect+repeller This post was edited by Kidddas53 at January 20, 2023 12:06 PM MST

Sometimes I kill them accidentally, but always go for the catch and release--no exception, from fruit flies to wasps.

catch and release 

Kill, mostly. Bees I shoo outside - or I get someone else to do it, I'm allergic. Spiders (which aren't bugs) I catch and release when my wife asks me to, otherwise I let them alone to do THEIR job of killing the bugs.
House flies and mosquitoes I hunt down relentlessly and destroy with extreme prejudice. Roaches I catch and feed to the spiders (the frogs get fed live crickets).

With rare exceptions,  I catch and release them.  I do kill  mosquitoes  with no remorse....