I uncovered a reason last week while studying John 13. In this chapter, Jesus is at a supper with His twelve disciples. He knows that very soon Judas will leave to betray Him. He knows that His death on the Cross is imminent.
Lovingly He shows His own the full extent of His love, in one manner by washing His disciples' feet. Including Judas' feet. The feet of His betrayer.
Why do that for the one destined to betray Him? Because the work shows the magnificence of His grace to even those who utterly reject Him. Washing the feet symbolized His work of cleansing us of the defilement of sin. He was evangelizing Judas by showing He alone could cleanse Judas of his sin.
Not only that, but the verse that struck me the most was verse 18a:
I am not referring to all of you; I know those I have chosen.
Jesus is saying that He knows those He has elected. And even so, He goes on in verses 20, 21, and 26 to by words and actions give an opportunity to Judas to repent. Every warning, every offer was a showing of His grace.
We are commanded to share the gospel of Jesus Christ, His salvation from sin, to all. For no one but Jesus knows His elect. And it is His very example to display His grace, even to those who do reject Him.
For then He and He alone is glorified in the offer of mercy, the work of justice.