Why couldn't Jimmy arrest Bob himself in "After Twenty Years"?

In "After Twenty Years," Jimmy's duty as a police officer is in conflict with his long history of friendship with Bob. Based on this story's very set-up—by which Bob and Jimmy had, twenty years earlier, made an arrangement to meet up after twenty years had passed—along with the fact that both men would proceed to uphold that earlier agreement, one must assume that their friendship was very close and that both men highly prized it. The fact that Jimmy finds himself unable to personally see to this arrest (and instead has to seek the intercession of a second policeman) further attests to the strength of that bond.
Furthermore, one should note that Jimmy himself seems to have had no apparent foreknowledge concerning Bob's criminal history. This revelation, when the two met face to face, would have likely resulted in no small degree of emotional turmoil.

When Jimmy encounters Bobby after their lives have diverged for 20 years, Jimmy is in perfect position to apprehend his friend for the crimes he had committed over the years. Unfortunately, he is unable to bring himself to do so, because of the close camaraderie they once shared. Their mutual history and deep friendship gives Jimmy pause, and though he knows the man deserves prison, he still sees him as the close friend he once knew and shared so much with.
Instead of letting him go, scot-free, Jimmy leaves and sends another officer to apprehend Bobby and reveal his identity. It hurts Jimmy too much to imprison his own friend, but he knows justice is more important than his feelings. So Jimmy does the right the the only way he is able to in that moment—by sending someone more detached to make the arrest.

In "After Twenty Years," Bob returns to New York, where he last saw his friend, Jimmy. When the two parted ways, they agreed to meet at a particular location in twenty years to see where life had taken them. As Bob waits for his friend, he encounters a police officer walking the street to ensure the shops are secured. Bob explains his presence to the police officer explaining that he is there waiting for a friend. It becomes obvious that Bob has been successful. Both his scarf pin and his watch contain diamonds. After a brief conversation, the police officer continues along his beat.
Finally, a man arrives in a trench coat and claims to be Jimmy. They greet each other and agree to go somewhere to talk. As they walk, Bob begins to share information about his career. When they come to a well-lit place, Bob discovers that the man in the trench coat is not Jimmy but is instead a police officer. The police officer calls him "Silky" Bob and tells him that he is wanted by the police in Chicago. Before taking Bob to the police station, the police officer hands him a note from Jimmy. Bob then realizes that Jimmy was the police officer he first encountered. In the note, Jimmy explains that he could not arrest Bob himself. While he does not give a reason for this, the reader can imply that Jimmy doesn't arrest Bob, because he values their friendship. However, while the friendship is important to Jimmy, he does not place it above the law. Jimmy sends the man in the trench coat, a plainclothes police officer, to arrest Bob instead.