Understanding these verses must begin with understanding Jesus' word usage. Remember when Jesus said of his dead friend Lazarus that he was sleeping? His disciples thought that Lazarus must be getting better if he were taking rest in sleep. But Jesus had to break it to them: Lazarus was dead.
Remember when Jesus spoke to the scribes and Pharisees saying they were as "whited sepulchres, which indeed appear beautiful outward, but are within full of dead men's bones, and of all uncleanness." (Matthew 23:27)? Obviously, dead bones in coffins aren't alive--yet he was addressing living persons. What then did it mean that he was ascribing "death" to these men? And how is it, by contrast, that of the deceased young lady, Jesus would say, "Why make ye this ado, and weep? the damsel is not dead, but sleepeth" (Mark 5:39)?
Jesus sees the heart. He sees the future of the soul. He knows that those who are alive spiritually will receive eternal life. In fact, John 3:36 indicates that eternal life can be ours even now, at present. Jesus spoke of Abraham, Isaac, and Jacob as being "alive" when he said: "I am the God of Abraham, and the God of Isaac, and the God of Jacob? God is not the God of the dead, but of the living." (Matthew 22:32)
Notice, too, that Jesus did not say "let the dead bury the dead." He said "let the dead bury their dead." In other words, let those who are spiritually dead bury those whom they consider "dead."
Once someone has physically died, there is no way to honor them by burying them--at least, they will never know of it. "The dead know not anything" (Ecclesiastes 9:5). To honor one's parents is not done by lipservice nor by courtesies or formalities, as many suppose. To truly honor one's parents is to live a life that will make them proud; to live in such a was as will not make them ashamed before others to have brought such a one into the world. Whether one attends the funeral or not is of small account in comparison with how he or she is living.
Jesus gives this instruction because the Father's interest is more for the living, who have hope of salvation, than for the dead, whose probation is past (see Ecclesiastes 9:4). To honor our Father in heaven, we must recognize this same principle.