Have you ever noticed how God almost casually states things that seem utterly impossible to man? He told Adam to name all the animals. He told Noah to build an ark (450 ft. by 75 ft.) when it had never been done before and it had never rained. He told Joshua to march around Jericho and shout to defeat an impenetratable fortress! He told Moses to speak to Pharaoh to let all his slaves go. Likewise Jesus often told His apostles to do "impossible" things: fear not in the storm, feed the crowd of 5000 with five loaves and two fish, even to heal the sick and raise the dead. He told believers to "Be holy." Throughout history God has instructed man to do seemingly impossible things.
However nothing compares with God's command, "Be holy, for I am holy." What could be more impossible than being holy like God? Furthermore, Hebrews 12:14 states that we should "Pursue peace with all people and holiness, without which no one will see the Lord." So not only does God command holiness, He declares that it is a necessity to see Him.
"Holy" is the essential character of God Himself. All created beings will cry "Holy, holy, holy" for eternity in God's presence. The word can be partially defined as "set apart, consecrated, pure, transcendent." The point is that clearly reaching this state or characteristic is impossible for man and his abilities. So the answer must be God. He has to do it. "With God all things are possible."
In the beatitiudes, or the declaration of the principles of God's Kingdom, Jesus stated, "Blessed are the pure in heart, for they shall see God." Matthew 5:8 These simple statements accentuate the qualities God wants us to desire and value as eternally important. Those "set apart, consecrated, pure in heart" ones will see God.
One of the principles of God's Kingdom is the working of our participation and God's power. When we seek Him with our whole heart, He will be found. When we draw near to Him, He draws near to us. When we forgive others He forgives us. So in the case of the qualities of the beatitudes and holiness, when we choose and seek these responses, we allow Him to do that work in us.
Jesus said in a little differently in John 12, "believe in the light that you may become sons of light." That belief or faith is further explained in Hebrews 11:6, "But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him." The point isn't God's holiness, or man's impossibility of attaining it by himself; but rather it is knowing and trusting that God will reward or come through for those who seek Him.
God calls us to be holy, we desire and choose to seek it, He does it in us. "He who calls you is faithful, and He will do it." 1 Thess 5:24 Be holy.