For "non-Christians", it might depend on if they have any religion or none. But let's say, for irreligious people, you could start with the basics: Is there a God, or isn't there a God? Do you believe in an afterlife with reward & punishment? Do you think all go to heaven? Or, if you believe in hell, what would one have to do to go there?
If there is no God, or no hell, then why should anyone be "good" to anyone else? If we all just evolved from apes, why can't we be like the lion in the jungle, and kill a gazelle when we're hungry? In other words, why can't we just do what we want, when we want, if there is no punishment for doing things like murder?
Or, you could ask, [think of some terrible crime:] Do you believe cold-blooded murder is wrong? Why? Make him justify his lack of belief in hell by contrasting it with some standard he does hold. And, kind of like with the protestant, we need an infallible Church with authority from God to know how to interpret the Bible, we also need an infallible Church with authority from God to know what the standards of behaviour should be. If there is no God, there is no standard, and why was anything the bad-guys of history [you could use either a villain like Mаο or Stаlin, or a favorite boogeyman from modern politics, HitIеr or Sаddаm Hussеin or Pυtin depending on your listener's opinions*] wrong or bad?
*It doesn't matter much how true a "villain" the example is, as long as said listener believes him to be a villain. Because you're trying to show that without an objective standard of morality, how do we judge anyone to be a villain?