In Leviticus 21:18, those people were not responsible for being that way. How can I explain this to others, especially that of a flat-nosed person?
Many of the laws regarding worship under the Old Testament existed because they symbolically represented something under the New Testament. Thus, sacrifices had to be without defect (e.g. Leviticus 1:3) because Jesus, who would be the sacrifice for the whole world, was without sin. A second reason is that defective animals are less valuable since they often cannot be used for breeding. God demands the best of men, not the leftovers that no one else wants.
"A son honors his father, and a servant his master. Then if I am a father, where is My honor? And if I am a master, where is My respect?' says the LORD of hosts to you, O priests who despise My name. But you say, 'How have we despised Your name?' You are presenting defiled food upon My altar. But you say, 'How have we defiled You?' In that you say, 'The table of the LORD is to be despised.' But when you present the blind for sacrifice, is it not evil? And when you present the lame and sick, is it not evil? Why not offer it to your governor? Would he be pleased with you? Or would he receive you kindly?" says the LORD of hosts. But now will you not entreat God's favor, that He may be gracious to us? With such an offering on your part, will He receive any of you kindly?" says the LORD of hosts. "Oh that there were one among you who would shut the gates, that you might not uselessly kindle fire on My altar! I am not pleased with you," says the LORD of hosts, "nor will I accept an offering from you" (Malachi 1:6-10).
The same problems apply to those serving the Lord. The High Priest represents Christ under the New Law. His lack of defect represented Jesus' lack of spiritual defect. The priests who serve God are of the best people Israel had to offer. Being a priest of God was not a job you got because you weren't useful for other tasks.
"Speak to Aaron, saying, 'No man of your offspring throughout their generations who has a defect shall approach to offer the food of his God. For no one who has a defect shall approach: a blind man, or a lame man, or he who has a disfigured face, or any deformed limb, or a man who has a broken foot or broken hand, or a hunchback or a dwarf, or one who has a defect in his eye or eczema or scabs or crushed testicles. No man among the descendants of Aaron the priest who has a defect is to come near to offer the LORD'S offerings by fire; since he has a defect, he shall not come near to offer the food of his God. He may eat the food of his God, both of the most holy and of the holy, only he shall not go in to the veil or come near the altar because he has a defect, so that he will not profane My sanctuaries. For I am the LORD who sanctifies them.'" (Leviticus 21:17-23).
In the church, each Christian is a priest (I Peter 2:9). We are commanded to be holy people (I Peter 1:13-16). We cannot serve God with spiritual defects (sin) (I Corinthians 6:9-10).
Thus, the Old Testament used physical things to represent spiritual truths found in the New Testament. It doesn't mean God was against people who had handicaps. However, He was trying to teach the Israelites the importance of serving God, and He used physical things to help them understand the spiritual concepts.