One can feel the anguish of David in verses 21-22 as he asks God, "Dear God, You know how much I hate those who oppose You, so why do You allow them to exist?" In other words, why don't You just wipe out those who still oppose Your will so I don't have to deal with them?"
There was a pledge of loyalty that ancient Near Eastern kings required of their vassals. In a similar fashion, David is acknowledging the fact that evil exists but he will choose to stand on the side of God and not the side of evil. There is this constant struggle as he still has to fight against those who oppose God's will.
No matter how nice we are, there is a constant uphill battle with evil in our present world. We must never let our guard down, not even for one minute. Furthermore, the rationale of today's Christian could be paraphrased, "I have my own problems to deal with. Why should I worry about strangers who oppose God? After all I know that God will win in the end, so why should I focus my energy on those who oppose His will? I don't sense anyone trying to kill me as I go out the door today."
Always remember that if we are doing God's will, evil forces exist that are going to try to make us a bad witness for Jesus. Although Satan can not take away our salvation, he seeks to do everything he can to twart the will of God and keep Christianity from spreading. He does what he can to make us a bad witness for God and that includes the idea of using people around us to focus on anything and everything other than making a difference for God in our lives.
The way we fight our own battles is by our dependency upon God for victory. We don't see or sense demons. We just know that we struggle through situations and with people who make it difficult for us to focus on God. We may ask God to wipe out those forces, but we also realize we are fighting them with His help.
The lesson here is that God does want to give us victory over such forces, but that victory comes by God working in us and through us. He is the One who will ultimately settle all wrongs and injustices.