Who Are These Dogs and Swine?

I recently received an email from one of my sisters-in-law asking me to share my thoughts about Matthew 7:6.  "Do not give dogs what is sacred; do not throw your pearls to pigs. If you do they may trample them under their feet,and then turn and tear you to pieces." (NIV)

So I shared with her the following observations:

- This aphorism is found in a cluster of unrelated teachings... part of the larger whole known as the "Sermon on the Mount" in Matthew's gospel - though it's not really much of a "sermon." It seems like Matthew has arranged some of the various collected teachings of Jesus into this grouping within his narrative.

-This aphorism is only found in Matthew's gospel.  Luke's very similar "Sermon on the Plain" does not include this teaching.

- Based on Matthew's frequent citation of Hebrew prophets and other factors in his writing, it is usually agreed that Matthew wrote his gospel for a Jewish audience - and it is in this context that the reference to dogs and pigs should probably be understood. Both dogs and pigs were considered unclean by the Jewish people.  Pigs were specifically forbidden and Dogs - though not explicitly defined as unclean -  were considered to be scavengers and carrion-eaters.

- And both were used as terms for Gentiles.

The somewhat softened interpretation of Jesus' words is usually said to be 'don't waste valuable things (scripture / participation in the holy) on those who are unable  or unwilling to appreciate them.'  But a more nuanced (and harsher) examination of this verse indicates that it was probably an injunction against sharing the gospel with Gentiles.

But that seems to stand very contrary to what Jesus actually did in his ministry (even as described in Matthew's gospel):  He shared the good news with a Roman Centurion, gentile demoniacs, and a Canaanite woman (whom Jesus even referred to as a "dog"...)

One early Christian writing (the Didache) applies this verse to the sharing of communion: "Let none eat or drink you Eucharist except those who have been baptized in the name of the Lord.  It was concerning this that the Lord said, 'Do not give to dogs what is holy.'"

I doubt very much that Jesus wanted us to be exclusionary with the gospel - he after all commissioned his disciples to take it to "all nations" (and "the nations" was often a euphemism for the Gentiles in the Hebrew bible).  So who are these dogs and swine?