What does Matthew 8:21 mean?

Two would-be disciples approach Jesus as His hand-picked group of twelve disciples prepare to get into a boat to cross the Sea of Galilee. The first one, a scribe, promises to follow Jesus everywhere. Jesus seems to warn the man that the road will be hard, since He is basically homeless. That, apparently, is not what this man expected, and he does not seem to pursue Jesus any further (Matthew 8:18–19).

Now another person approaches Jesus. Not everyone described in Matthew as a disciple or follower of Jesus is necessarily one of His chosen twelve. The terms have a literal meaning that's not exactly the same as those terms as used in the context of the modern church. Some who followed Jesus from place to place and believed His teaching may have been referred to as disciples, as well. Since Jesus has just made a remark about the hardship of His ministry life, it's unclear whether this person is one of the Twelve or someone new.

This man seems to think that Jesus expects Him to follow Him immediately. The man responds to this call with an answer of "yes, but…" He asks the Lord to allow him to go and first bury his father, implying that he will follow Jesus after that. Commentators suggest this man's father may not have yet died. Or it's possible that he had died, and the man was talking about the Jewish custom of reburying a loved one's bones a year after passing. In other words, this disciple may have been requesting to delay his role as a follower of Jesus for a year or longer. This was to fulfill what custom and tradition expected from sons, especially firstborn sons.

Jesus will not agree to this request. Cultural expectations are not meant to override God's will for a person's life.