The second phrase in this verse is eye-opening. Those who thought they would inherit the Kingdom, all the Pharisees, scribes, and teachers of the Law, want nothing to do with it. It didn't match their narrative. Instead, the sinners, publicans, non-elites, even violent people are taking hold of the Kingdom. The old English aristocracy would call them the "vulgars." The vulgars are raiding the Kingdom of God!
This is consistent with one of the parables of Jesus in Luke 14:15-24, the story of the man who prepared a banquet for his friends and acquaintances. When invited, many of them began making excuses for not attending. So the man sent his servants out to go get anyone wandering the streets, the vulgars, if you will, to take the place of those who were invited.
The Kingdom of God is for the poor -- the poor in spirit. What did Jesus say in the opening sentence in his Sermon on the Mount? "Blessed are the poor in spirit, for theirs is the kingdom of heaven." Who is poor in spirit? It often has nothing to do with money, although those with lots of money often fail to recognize their poverty of spirit. The religious elite are seldom poor in spirit. Their arrogance often bars them from entering the Kingdom.
Poor in spirit simply means that one recognizes that one doesn't have God figured out. Legalism is one of the most common things that will bar someone from the Kingdom. If you find that circumstances are challenging your ideas of God, your rules for Christian living, your religious dogma, then you should be happy. God is trying to make you poor in spirit so that you can be part of his Kingdom.