Although he was showing more concern for himself than compassion for Jesus, Pilate does show some conflicted feelings here.
Meanwhile Jesus stood before the governor, and the governor asked him, "Are you the king of the Jews?" "Yes, it is as you say," Jesus replied. When he was accused by the chief priests and the elders, he gave no answer. Then Pilate asked him, "Don't you hear the testimony they are bringing against you?" But Jesus made no reply, not even to a single charge—to the great amazement of the governor.
Now it was the governor's custom at the Feast to release a prisoner chosen by the crowd. At that time they had a notorious prisoner, called Barabbas. So when the crowd had gathered, Pilate asked them, "Which one do you want me to release to you: Barabbas, or Jesus who is called Christ?" For he knew it was out of envy that they had handed Jesus over to him.
While Pilate was sitting on the judge's seat, his wife sent him this message: "Don't have anything to do with that innocent man, for I have suffered a great deal today in a dream because of him."
But the chief priests and the elders persuaded the crowd to ask for Barabbas and to have Jesus executed.
"Which of the two do you want me to release to you?" asked the governor. "Barabbas," they answered.
"What shall I do, then, with Jesus who is called Christ?" Pilate asked. They all answered, "Crucify him!"
"Why? What crime has he committed?" asked Pilate. But they shouted all the louder, "Crucify him!"
When Pilate saw that he was getting nowhere, but that instead an uproar was starting, he took water and washed his hands in front of the crowd. "I am innocent of this man's blood," he said. "It is your responsibility!"
All the people answered, "Let his blood be on us and on our children!"
Then he released Barabbas to them. But he had Jesus flogged, and handed him over to be crucified. Matthew 27:11-26
I notice you put in the "let his blood . . . " which appears only in one gospel and has been used as a blood libel against Jews for centuries. Very clever of you. The Romans won the wars, and the RC Church became the ROMAN Catholic Church and the official church of the empire. There was more to risk by offending the ROMANS than the Jews. Got it?
There is no evidence that Pilate every showed mercy anybody in his entire life. Likewise, it ws not a CUSTOM to release a prisoner during the Passover. No proof whatsoever. IF you want to drink the kool-aide and believe it, that is your problem.