My mother didn't like spiders either. I don't mind them at all - I just let them scurry into my hand, cover them with the other hand so they don't escape, carry them outside the house, and gently release them. I don't like harming any insect. If a fly or wasp or bee flies into the house into a room, I shut the door, then open the window and wait for it to fly out.
That's what middle son does.
I miss him as my Chief Spider Catcher, now he has left home.
I can catch daddy longlegs and release them.
I'm not keen on wasps because I have had mild allergic reactions to their stings, otherwise I don't mind other insects.