Well you might be crazy, but that’s besides the point. You can’t stop photos from saving when taken in iMessage. it was added in iOS 10 or 11, I forgot when. I wish Apple would at least give us an option. I know I’ve been waiting.
Are you using iMessage? If I copy a photo from the web and send it to someone it doesn’t download to my photo library. WhatsApp however has this behavior, which can be changed in its settings: