The idea that the wise men offered gold because the newborn is a king, incense because he is God, and myrrh because he is mortal is attested as far back as the fourth century, e.g. in an Epiphany poem by Aurelius Prudentius Clemens published in his Liber Cathemerinon.
The reputation of myrrh as a “bitter perfume” which speaks
of the death of Christ can be anchored in the two other occurrences of myrrh in
the Gospels. In Mark 15:23 “they offered him wine mixed with myrrh” on the cross and in John 19:39 Nicodemus
brought “a mixture of myrrh and aloes” to embalm the dead body. The fact that
neither of these is in Matthew’s gospel makes it difficult to claim that this
is what the evangelist had in mind in Matthew 2.
Others say that the gifts speak of Christ as king,
priest and lover. About half of all occurrences of myrrh in the Bible are
in the Song of Songs. Strikingly, here and in Psalm 45 myrrh is a man’s perfume
as well as a woman’s. More commonly, myrrh is something women use to attract
men, e.g. in Proverbs 7:17 and Esther 2:12. But myrrh was also an ingredient in the anointing
oil for priests (Exodus 30:23).
In fact, Song of Songs 3 and Exodus 30 seem to be the only
two places prior to Matthew 2 in which gold, frankincense and myrrh come
together. With Song of Songs 3 in mind we may think of gold, frankincense and myrrh as heralding the arrival of
a king who is love.
Exodus 30 presents us with a gold-covered wooden altar which
is as much anointed with myrrh as the priests and on which frankincense-containing
incense is burnt. Chris Hamer-Hodges argues on that basis that the gifts speak of God’s presence:
"Frankincense was made into incense used by the high priest when he entered before the presence of God.
Myrrh was made into the holy anointing oil used on God's prophets, priests and kings.
Gold was used to cover everything in the temple that communicated the glorious presence of God himself."