A complete lack of fear of one's enemies is a highly desirable thing. There's nothing these people can do to me? Great! But the Bible never promises invincibility. Sure, God can deliver us from any enemy. He can overthrow entire nations, He can certainly protect you. But sometimes, that's not exactly what He intends to do.
But the great thing for Christians is that there's nothing we can lose that we can't be paid back a hundred times over. In this life, we can lose a lot of things. Money, property, friends and family, even our very lives, all of which we would ultimately lose anyway because that's just the world in which we live. But with God, even death is not a loss, because we have eternal life.
But man is not the only enemy we can encounter on this planet. There is an enemy far greater than any man, or any beast. That enemy is Satan, and he hates you enough to want you to spend an eternity in Hell. But David, lead by the Spirit, informs us that we don't need to fear him either. Who is this spindly little serpent that dares try to separate us from God? He talks a big game, and indeed, he can be dangerous if we're foolish enough to let him be. But as long as God is your refuge, he's got about as much strength as a goldfish in the desert.
James tells us that if we resist the devil, he will flee from you (James 4:7). Of course, there is a catch. On our own, we are very much vulnerable to the devil. But there is nothing more terrifying to him than a Christian who submits himself to the Lord. Therefore, submit, and you, too, will be able to say "The Lord is the strength of my life; of whom shall I be afraid?"
Recommended song: God is for us - ALM UK