It is absolutely vital to remember that this play is as much about the makings of a perfect king as it is about anything else. Henry has a lot to prove. Remember how he was famed for his dissolute days with Falstaff and how he disappointed his father. Now, he is the King of England, and as such, he needs to show that he can act like a King. This of course involves incredible harshness when necessary. In Act II scene 2 this does become necessary, as his three most trusted friends, Grey, Scroop and Cambridge have been found out to be traitors and Henry must face them, administering justice.
He does this by giving them a hypothetical situation and asking for their opinion: should he show mercy to a man that drunkenly insulted him? Although he is inclined to show mercy, his three friends all strongly advise him to punish the man harshly. However, as he hands them the papers with the information about their treachery on it, and they plead for mercy, he tells them that:
The mercy that was quick in us but late
By your own counsel is suppressed and killed.
Henry has to show himself strong and unyielding. His personal attachments must not enter into what he does as King here. We can almost see the other faithful advisers in this scene, Bedford, Exeter and Westmore-Land, watching carefully whether Henry is able to administer the justice that he needs to administer on his friends, especially his former "pillow-fellow," Scroop. Some productions have Henry really upset and torn in this scene, doing what he knows he has to do, yet angry with his former friends for putting him in this impossible situation. Either way, this scene is an important part of Henry's path to becoming the perfect King.