Answer: Before answering the questions as to why Jesus said "Father forgive them . . ." we need to understand WHY came to earth in the first place.
One main reason (of many) Jesus came in the flesh to Earth is so that all of humanity might have their sins washed away and have the opportunity to be at one with Him and the Father. Most people do not understand why we need God to forgive us, but we ALL do, whether Christian or not.
The Jewish leadership who had Jesus crucified, even though knowing all the prophecies regarding the Savior, was blind themselves as to who He really was. Therefore, in their own minds, they were executing a blasphemer, which was the legal thing to do under their law.
What was illegal was the fact that the Jews had the trial at night with false witnesses, a "kangaroo court" if you will, because they feared the people. Now, let us look at a few Scriptures and get the context of the forgiveness Jesus requested of the Father.
And when they had come to the place called Calvary (also known as Golgotha or the place of the skull), there they crucified Him . . . Then Jesus said, 'Father, forgive them, for they do not know what they do' (Luke 23:33 - 34).
Since those who were killing him were deceived, and did not understand what they were doing, Jesus asked God the Father to forgive their sin. This implies very strongly that someday all will know the full extent of what they did. It will be at that time that repentance will come. Read Jesus' statement in Matthew 23 where he bemoans Jerusalem's rejection and the fact that the city would soon be left desolate. This prophecy was fulfilled in 70 A.D. when Roman troops took the city, destroyed it, and burned down the temple.
Scripture states that someday every knee will eventually bow and every tongue will confess that Jesus is their Savior.
Therefore, God (the Father) has also highly exalted Him and bestowed upon Him a name which is above every name; That at the name of Jesus every knee should bow, of beings in heaven and on earth and under the earth, And every tongue should confess that Jesus Christ is Lord to the glory of God the Father (Philippians 2:9 - 11).
In the eleventh chapter of Romans, the Apostle Paul states that God will not ultimately cast away or reject His people (Israelites and Jews) whom He foreknew.
Now then I say, did God Himself repudiate His people? MAY IT NEVER BE! For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin. God did not repudiate His people whom He foreknew . . . (Romans 11:1 - 2, HBFV)
Jesus said "Father forgive them . . ." because he was aware that every person, in His own time, would have a chance to fully repent and receive eternal life. In what the Bible calls the second resurrection, those who killed Christ will have their spiritual blindness taken away from their hearts and given a chance to repent.