Was Judas Jesus' friend?

Whenever we read of Matthew's story of Jesus' arrest, we will always be puzzled by the way Jesus addressed Judas. Here is Matthew's account.
Now the betrayer had given them a sign, saying, "The one I shall kiss is the man; seize him."
And he came up to Jesus at once and said, "Hail, Master!" And he kissed him.
Jesus said to him, "Friend ἑταῖρε, why are you here? ἐφʼ ὃ πάρει " Then they came up and laid hands on Jesus and seized him (Matthew 26:48-50).
In this story, we have located the origin of the famous phrase "Judas' kiss". But why did the Jesus of Matthew call Judas friend?
Mark was the first to tell the story. In his version, Jesus said nothing.
Now the betrayer had given them a sign, saying, "The one I shall kiss is the man; seize him and lead him away under guard."
And when he came, he went up to him at once, and said, "Master!" And he kissed him.
And they laid hands on him and seized him (Mark 14:44-46). Matthew added this 'friend' statement of Jesus. What about Luke?
Luke does not mention the pre-defined signal and Jesus made a different statement.
While he was still speaking, there came a crowd, and the man called Judas, one of the twelve, was leading them. He drew near to Jesus to kiss him;
but Jesus said to him, "Judas, would you betray the Son of man with a kiss?" (Luke 22:47-48)In Luke, there are 3 persons who kissed: Mary who washed Jesus' feet with her tears and kissed them; the father who kissed the repentant Prodigal Son and Judas who kissed Jesus. In the arrest story, Luke asked all the disciples of Jesus why they would betray him in the name of love. This is an altogether different spirituality.
In the arrest story of John, there is not even a trace of Judas' kiss. Jesus simply surrendered himself. So, let us return to Matthew to explore this ἑταῖρε. A search of ἑταῖρε in the Greek New Testament yields only 3 results: Matthew 20:13, Matthew 22:12 and Matthew 26:50, all in Matthew! How lucky!
Matthew 20 tells us the parable of the vineyard owner who hired workers at different hours of the day. At the end of the day, he paid each of them a denarius, those who had worked for just one hour and those who had worked since the early hours. When they complained,
But he replied to one of them, `Friend, I am doing you no wrong; did you not agree with me for a denarius?
Take what belongs to you, and go; I choose to give to this last as I give to you.
Am I not allowed to do what I choose with what belongs to me? Or do you begrudge my generosity?'
So the last will be first, and the first last." (Matthew 20:13-16) When Jesus called Judas 'friend', Jesus told Judas that he was doing Judas no wrong!
Matthew 22 tells us yet another parable of the Kingdom of Heaven, the king's marriage feast for his son. Many were invited but did not come. So, the king sent his servants to gather all they could find, both good and bad, to fill the wedding hall.
"But when the king came in to look at the guests, he saw there a man who had no wedding garment; and he said to him, `Friend, how did you get in here without a wedding garment?' And he was speechless.
Then the king said to the attendants, `Bind him hand and foot, and cast him into the outer darkness; there men will weep and gnash their teeth.'
For many are called, but few are chosen." (Matthew 22:11-14)When Jesus called Judas 'friend', Jesus asked why he had ended up in this state. He was called into the Kingdom of Heaven, but in the end, not chosen. Poor Judas.

My God, You are generous and do us no wrong. It is our fault not to have made the best out of this opportunity to enter into Your eternal life. We are only to blame. Have mercy and grant us more time so that we can make an appropriate wedding garment to enjoy Your banquet. Amen.