Why would Jesus use drinking blood, an unclean act, as a symbol for communion?

Actually, the symbolic physical act was drinking wine, as in the OT Passover meal. In the communion, the wine represents the blood of Jesus. Jesus used wine as a symbol for his blood, which signified his sacrifice on the cross. He was the Lamb of God of the Passover, taking away the sins of the world.

Leviticus 17:

11 For the life of the flesh is in the blood, and I have given it for you on the altar to make atonement for your souls, for it is the blood that makes atonement by the life.

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What about the partaking of the blood?

Again, we are not talking about drinking physical blood.

John 6:

55 For my flesh is true food, and my blood is true drink. 56 Whoever feeds on my flesh and drinks my blood abides in me, and I in him.

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The physical life of the physical flesh is in the physical blood. The animated life of the human spirit is in the precious blood of Jesus. Communion is one collective way to feed our human spirits. It grows and strengthens our spiritual life. This is not just a metaphor or symbol. This is a spiritual reality. Believe it.

Why would Jesus use drinking blood as a symbol at all since it is misleading?

It was a radical idea and easily misunderstood as some form of cannibalism. It tested the loyalty of the listeners. John 6:

60 When many of his disciples heard it, they said, “This is a hard saying; who can listen to it?”

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They left Jesus.

65 And he said, “This is why I told you that no one can come to me unless it is granted him by the Father.” 66 After this many of his disciples turned back and no longer walked with him. 67 So Jesus said to the twelve, “Do you want to go away as well?” 68 Simon Peter answered him, “Lord, to whom shall we go? You have the words of eternal life, 69 and we have believed, and have come to know, that you are the Holy One of God.”

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The loyal ones passed the test. They stayed.

This test continues today. Some pass, and some fail. If one digs deeper into the symbolism and typology, he will find the deeper significance of spiritual reality, as I have tried to do in this OP. Communion feeds the participants' human spirits to strengthen them into the Oneness of the Body of Christ.

Have you passed this loyalty test?