Your example does not use the phrase "pitch on." "Pitch him" is not a collocation or a phrasal verb. It's simply a use of a verb, "to pitch," with a direct object, "him."
"Pitch" is a word with a long list of meanings. One of them is a noun, short for "a sales pitch." It means a presentation intended to convince someone to buy something. It suggests something that is short and intense.
I first heard it used with respect to circuses and carnivals. The "pitchman" stands in front and delivers the "pitch" in a loud voice. He wants to get people walking by to stop and buy something.
Nowadays, it can mean a few phrases you say to someone in an elevator to tell them quickly why they should hire you, or buy your company's services. It can also mean a presentation in a meeting room, with PowerPoint slides, trying to convince a group of people to buy something or agree to something.
As is common in English, we have related meanings of the same word as a noun ("a ten-minute sales pitch") and a verb ("On Tuesday, I'm pitching them on our new product line.")
"To pitch him" means "to tell him, quickly and convincingly, why he should hire you" (or buy something from you).
I imagine it comes from the meaning of "to pitch" meaning "to throw something with force and speed." In US baseball, the pitcher pitches the ball to the catcher. In a sales pitch you are "throwing" words at someone.