Another way of looking at Matthew 6 is to see it as ultimately being addressed to the early churches, the members of what I've been calling the "Jesus Movement." It presents a charter for life in the new society they were creating in the first century, which was based on the teachings of Jesus. Summarized most simply, Jesus taught to cease grasping after things. Stop grasping after public recognition. Stop showing off your piety. Stop grasping after wealth. And in the opening verses of Matthew 7, he taught to stop grasping after self-affirmation by tearing down others. Stop, in sum, building yourself up so you can feel important and "get ahead" of everyone else. Jesus' words about God and possessions (6:24-34) sum up the matter: don't stress out over having material goods and enough food. Stop grasping and grabbing for self-advancement.
In the last posting, I suggested that Matthew 6 could be seen as a dig at the wealthy of Jesus' day who did invest themselves in grasping after just these things. Jesus himself may indeed have been speaking to the Pharisees and Sadducees, at least in part; but the author/compiler of Matthew would surely have seen that these teachings were crucial to building faithful, loving Christian communities in the early decades of the Jesus' Movement. Grasping, greedy individuals disrupt their communities; they are a pain to people around them. They represent what is most reprehensible in human society, and people resent them for their greedy need for attention and the way they treat people around them.
That is why the author concluded with words from Jesus that warned early Christians to stop judging others including each other. Stop your greedy, grasping self-aggrandizement by tearing down others. Get rid of the log in your own eye and then help others remove the specks in their eyes. To summarise this whole point about grasping, the author then quoted Jesus' teaching that we shouldn't give what is holy to dogs or throw our valuables into a pigsty. That is exactly what we do when we "Grab for all the gusto you can get," as the old beer commercial put it. Grasping behaviors come back to bite the greedy—and those around them. They had no place in the new society of the early church. There was a better way of doing things, and it was to that better way that the compiler/author next turned. Stay tuned.