There doesn't seem to be a generally accepted explanation for the use of the dove as representing the Holy Spirit. We are dealing with a question of interpreting a symbol that is not common in the Bible.
      In the ancient Near East, doves sometimes represented pagan goddesses. In Egypt the "soul" of the deceased took the form of a bird, usually a dove, as it departed to the heavens. This symbolism is totally foreign to the Old Testament; doves are never a symbol of God.
      However, an examination of the symbolic usages of the dove in the Old Testament could be of help in understanding its symbolic function at Jesus' baptism (Matt. 3:16).
      1. Symbol of Mourning: The low and soft cooing of the dove gave the impression to the hearers that it was lamenting or mourning, and it became a symbol for that human experience. During Hezekiah's illness he said, "I moaned like a mourning dove" (Isa. 38:14).* Those who survive the attack of Babylon "will be . . . moaning like doves of the valleys" (Eze. 7:16). The prophet writes, "We all growl like bears; we moan mournfully like doves" (Isa. 59:11).
      2. Symbol of Vacillation: The dove flies to and fro, giving the impression that it is disoriented or vacillating with respect to its destiny. This characteristic of the bird became a fitting symbol for the indecisiveness of Israel, its lack of commitment to the Lord: "Ephraim is like a dove, easily deceived and senseless—now calling to Egypt, now turning to Assyria" (Hosea 7:11).
      3. Symbol of Love: The dove's beauty and its traditional faithfulness to its mate were taken by the ancients to be a symbol of human love and beauty. This is particularly the case in the Song of Songs: "My dove in the clefts of the rock, in the hiding places on the mountainside, show me your face, let me hear your voice" (2:14); "Open to me, my sister, my darling, my dove" (5:2; cf. 1:15; 4:1). Christ commanded the disciples to express in their lives the love and gentleness of the dove (Matt. 10:16).
      4. Symbol of Deliverance: The rapid flight of the dove became a symbol of deliverance from one's enemies or from threatening circumstances. The psalmist writes: "Oh, that I had the wings of a dove! I would fly away and be at rest" (55:6). The Israelites returning from the Exile are described as those "that fly along like clouds, like doves to their nests" (Isa. 60:8; cf. Hosea 11:11). Probably the most important symbol of deliverance was the dove sent by Noah from the ark that came back with an olive branch in its beak (Gen. 8:10-12). It was a sign of peace; the storm was over.
      Which of those meanings is expressed through the symbolic use of the dove at the baptism of Jesus? We can easily eliminate the first two because they express the negative side of the symbol. It is also clear that according to Matthew 3:16 the dove is a visible expression of the anointing presence of the Spirit.
      But why the dove? The words spoken by God at that moment help us to understand the symbolism. He said, "This is my Son, whom I love" (verse 17). The symbol of love, the dove, and the word of love merged in the experience of the baptism of Jesus. God's love was flowing down to His Son as a member of the human race. In Christ a channel was found through which God's love could reach us; He was anointed to function as the only means through which God's grace is available to us.
      One could also argue that the dove is, in this particular case, a symbol of deliverance. The dove as a symbol of the love of God appeared, telling us that, as with the Flood, the storm of sin is not powerful enough to keep us permanently separated from the Father. Our planet is now connected with heaven through Christ. In accepting His Son, God signifies to us that we are also accepted in the Beloved through faith in the provision He made on our behalf.