Non-Christians and Unadopted Puppies

Have you ever noticed that many Christian people talk about "non-Christians" the same way we talk about unadopted puppies?

"You need to befriend one."

"They need you to take an interest in them."

"Be intentional when them."

"If you don't love them, who will?"

Maybe that's why in Luke 10, Jesus never answers the man's question "Who is my neighbor?" Instead, Jesus tells the guy a story inviting him to be a neighbor whomever he is around. Seems to me that it is important for us to live the Christ-centered life around everyone we meet - not to show extra kindness to a group of people who meet a certain narrow definition.