Here are the first 10 verses:
1 My God, my God, why have you forsaken me?
Why are you so far from helping me, from the words of my groaning?
2 O my God, I cry by day, but you do not answer;
and by night, but find no rest.
3 Yet you are holy, enthroned on the praises of Israel.
4 In you our ancestors trusted; they trusted, and you delivered them.
5 To you they cried, and were saved; in you they trusted, and were not put to shame.
6 But I am a worm, and not human; scorned by others, and despised by the people.
7 All who see me mock at me; they make mouths at me, they shake their heads;
8 “Commit your cause to the Lord; let him deliver—let him rescue the one in whom he delights!”
9 Yet it was you who took me from the womb; you kept me safe from my mother’s breast.
10 On you I was cast from my birth, and since my mother bore me you have been my God.
Take for example, the second verse:
O my God, I cry by day, but you do not answer
How do you explain that this is something that God would have said?
Also in verse 6, why would God say that He is a worm?
Why just the first ten verses? You must read the whole Psalm, especially its conclusion.
But you, O Lord, do not be far off!
O you my help, come quickly to my aid!
20 Deliver my soul from the sword,
my precious life from the power of the dog!
21 Save me from the mouth of the lion!
You have rescued[c] me from the horns of the wild oxen!
22 I will tell of your name to my brothers;
in the midst of the congregation I will praise you:
23 You who fear the Lord, praise him!
All you offspring of Jacob, glorify him,
and stand in awe of him, all you offspring of Israel!
24 For he has not despised or abhorred
the affliction of the afflicted,
and he has not hidden his face from him,
but has heard, when he cried to him.
25 From you comes my praise in the great congregation;
my vows I will perform before those who fear him.
26 The afflicted shall eat and be satisfied;
those who seek him shall praise the Lord!
May your hearts live forever!
27 All the ends of the earth shall remember
and turn to the Lord,
and all the families of the nations
shall worship before you.
28 For kingship belongs to the Lord,
and he rules over the nations.
29 All the prosperous of the earth eat and worship;
before him shall bow all who go down to the dust,
even the one who could not keep himself alive.
30 Posterity shall serve him;
it shall be told of the Lord to the coming generation;
31 they shall come and proclaim his righteousness to a people yet unborn,
that he has done it. (ESV)
When Jesus quoted the first line of Psalm 22, his listeners, who were Jews knew what he was referring to. Psalm 22 tells of a man who felt abandoned by God and friends but if you read through to the end, you see that God pulls through for him. Jesus is not crying out in despair; he is applying this Psalm to himself. Bearing the sins of all mankind, he can easily feel abandoned by God, which is what sin does; it separates us from God. Not his own sins of course but ours; he became sin for us. But beyond this feeling of abandonment, Psalm 22 ends with a note of victory.
So no, this cry from the cross does not disprove Jesus’ divinity at all. If anything, it only proves his humanity. True God, true Man.