I very much like @JamesT's answer, and also disagree with it. Here is where I agree:

God is free. He was under no compulsion to create us, and after we sinned, was under no compulsion to save us. In our desire to worship God's omnipotence and wisdom, it is fitting to ascribe to him the capability of identifying a multitude of ways by which his power and love might accomplish the task. However, he has communicated to us the necessity of some things that he has done. Here are a few ways that God has informed us about necessary things:

Isaiah 63:

4 It was for me the day of vengeance; the year for me to redeem had come. 5 I looked, but there was no one to help, I was appalled that no one gave support; so my own arm achieved salvation for me, and my own wrath sustained me. 6 I trampled the nations in my anger; in my wrath I made them drunk and poured their blood on the ground.”

If God desires that salvation be accomplished, he must do it. The savior must be God.

In Luke 22:

41 He withdrew about a stone’s throw beyond them, knelt down and prayed, 42 “Father, if you are willing, take this cup from me; yet not my will, but yours be done.” 43 An angel from heaven appeared to him and strengthened him. 44 And being in anguish, he prayed more earnestly, and his sweat was like drops of blood falling to the ground.

The cup that Jesus begs to avoid is his death. What father, loving his Son infinitely, on hearing a tearful plea from a Son who has honored him with perfect obedience and love, would reject such a plea if it were optional? The necessity is here made emotional, visceral, and wholly without doubt.

In Genesis 22, another father who passionately loved his son met a different fate:

6 Abraham took the wood for the burnt offering and placed it on his son Isaac, and he himself carried the fire and the knife. As the two of them went on together, 7 Isaac spoke up and said to his father Abraham, “Father?”

“Yes, my son?” Abraham replied.

“The fire and wood are here,” Isaac said, “but where is the lamb for the burnt offering?”

8 Abraham answered, “God himself will provide the lamb for the burnt offering, my son.” And the two of them went on together.

9 When they reached the place God had told him about, Abraham built an altar there and arranged the wood on it. He bound his son Isaac and laid him on the altar, on top of the wood. 10 Then he reached out his hand and took the knife to slay his son. 11 But the angel of the Lord called out to him from heaven, “Abraham! Abraham!”

“Here I am,” he replied.

12 “Do not lay a hand on the boy,” he said. “Do not do anything to him. Now I know that you fear God, because you have not withheld from me your son, your only son.”

13 Abraham looked up and there in a thicket he saw a ram[a] caught by its horns. He went over and took the ram and sacrificed it as a burnt offering instead of his son. 14 So Abraham called that place The Lord Will Provide. And to this day it is said, “On the mountain of the Lord it will be provided.”

We are shown two times: one when an alternate sacrifice was available, and one where an alternate sacrifice was not. The sacrifice of Jesus was not optional.

When Jesus met the two men on the road to Emmaus in Luke 24, he said this:

25 He said to them, “How foolish you are, and how slow to believe all that the prophets have spoken! 26 Did not the Messiah have to suffer these things and then enter his glory?” 27 And beginning with Moses and all the Prophets, he explained to them what was said in all the Scriptures concerning himself.

Jesus himself that the Messiah had to die, and that the whole Old Testament said the same thing. In John, 15:13, Jesus said:

13 Greater love hath no man than this, that a man lay down his life for his friends.

Could Jesus choose not to be our friends? Could he choose not to love to the uttermost degree? If God decided to befriend even one human, and decided to love even one man or woman, being one who shows infinite love, if that friend sinned and needed a savior, then Jesus had to die.

So did Jesus, the Son, have that choice? IN John 10, Jesus says:

11 “I am the good shepherd. The good shepherd lays down his life for the sheep. 12 The hired hand is not the shepherd and does not own the sheep. So when he sees the wolf coming, he abandons the sheep and runs away. Then the wolf attacks the flock and scatters it. 13 The man runs away because he is a hired hand and cares nothing for the sheep.

14 “I am the good shepherd; I know my sheep and my sheep know me— 15 just as the Father knows me and I know the Father—and I lay down my life for the sheep. 16 I have other sheep that are not of this sheep pen. I must bring them also. They too will listen to my voice, and there shall be one flock and one shepherd. 17 The reason my Father loves me is that I lay down my life—only to take it up again. 18 No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again. This command I received from my Father.”

The father commanded Jesus to take care of the sheep that he had given to him. In John 17, he speaks more plainly:

6 “I have revealed you[a] to those whom you gave me out of the world. They were yours; you gave them to me and they have obeyed your word. 7 Now they know that everything you have given me comes from you. 8 For I gave them the words you gave me and they accepted them. They knew with certainty that I came from you, and they believed that you sent me. 9 I pray for them. I am not praying for the world, but for those you have given me, for they are yours. 10 All I have is yours, and all you have is mine. And glory has come to me through them. 11 I will remain in the world no longer, but they are still in the world, and I am coming to you. Holy Father, protect them by the power of your name, the name you gave me, so that they may be one as we are one. 12 While I was with them, I protected them and kept them safe by that name you gave me. None has been lost except the one doomed to destruction so that Scripture would be fulfilled.