The original Greek of John 19:22 is:
Ὃ γέγραφα, γέγραφα = "What I have written, I have written".
[This is accurately translated by the equivalent Latin, Quod scripsi, scripsi.]
There have been various interpretation of Pilate's outburst; these include:
- Stubbornness
This is best expressed by Ellicott:
This was a mere piece of obstinacy. Pilate knew that he had
prostituted his office in condemning Jesus, and he revenged himself
for weak compliance by ill-timed mulishness. A cool-headed governor
would have humoured his difficult subjects in such a trifle, as a just
one would have been inflexible in a matter of life and death. But this
man’s facile yielding and his stiff-necked obstinacy were both
misplaced. ‘So I will, so I command. Let my will suffice for a
reason,’ was what he meant. He had written his gibe, and not all the
Jews in Jewry should make him change.
- Pricked Conscience
For all his (many) faults, Pilate at least (partially?) recognized in Jesus a vastly different character from the usual run of criminals and felons that paraded through his court-room. He appears to see that Jesus is no mere man, and something greater than a man and certainly not guilty. In this action of the cross titulus, perhaps Pilate is attempting to both recognize Jesus for who He is and thus rebuke His accusers.
Bengel succinctly says this:
Pilate’s thought was to consult for the honour of his own authority:
he really hereby subserved the Divine authority.
However, Bengel then ventures an even greater opinion:
In the person of the Procurator (Governor) himself something of a
prophetical character was in this instance vouchsafed, as in the case
of the High Priest, ch. John 11:51, Caiaphas: “One man should die for
the people. This spake he not of himself; but being High Priest that
year, he prophesied.
- Exercise of Authority
Pilate's outburst was a snub to the Jews whom he clearly disliked and "stamp of the foot" for his own Roman authority
- An Insult to the Jews
The pulpit commentary expresses this view:
Pilate answered, What I have written I have written. And he curtly
dismissed them. Pilate no longer dreaded their making his apparent
favor to Jesus into a complaint to the emperor, and he gave way to the
indomitable temper of which Philo accuses him. He found grim
satisfaction in insulting and browbeating them for a moment, {Ο
γέγραφα γέγραφα. "I said it, and I meant it; I have crucified your
King; yes, true King in his own sense, but not in yours. You have
falsely charged him with rebelling against Caesar, and you know that
you have lied to my face. Let be; he is your King, and so perish all
your futile attempts to shatter the arm that holds you now in its
grasp." That and more was condensed in this haughty and obstinate
reply. While this was going on in the Praetorium, the tragedy was
proceeding at Golgotha; and St. John now returns thither, and
describes an event of intense interest which occurred, as all
synoptists say, at the very time of the elevation of the cross. John,
however, has further facts and symbolic detail to append which were
omitted by them. John 19:22
For what it is worth, I am of the opinion that Pilate's motives were a combination of all of the above.
The Jamieson-Fausset-Brown Bible Commentary offers this:
Stung by this, the Jewish ecclesiastics entreat that it may be so
altered as to express, not His real dignity, but His false claim to
it. But Pilate thought he had yielded quite enough to them; and having
intended expressly to spite and insult them by this title, for having
got him to act against his own sense of justice, he peremptorily
refused them. And thus, amidst the conflicting passions of men, was
proclaimed, in the chief tongues of mankind, from the Cross itself and
in circumstances which threw upon it a lurid yet grand light, the
truth which drew the Magi to His manger, and will yet be owned by all
the world!