I was curious. The thing about Benny, is that he isn't a raider. He's well-spoken, dresses way too nicely, and appears to have a larger plan contingent on something he knows that you don't. That was enough to compel me to chase him, to find out why such a city slicker was mucking out in the country - and why he would believe the consequences of stealing from the Courier would be worth it.
Curiousity, revenge, fulfilling your contract, self-preservation etc.
Because the Courier was delivering something to MISTER HOUSE, delivering in-fact the one thing he wanted in the world; likely there was a lot of money involved and likely his professional reputation if he wanted to keep working in California.
Oh yeah and Benny shot you in the face.
The courier has some back-story we glean from Lonesome Road, and he doesn't seem like the person to not be proactive or shy away from violence as-well as being a life-long Courier who's handled some very important packages for people - notably for the NCR government transporting some seriously important tech. This ties again in why the professionalism angle. The guys got a rep in California, he's not going to be the guy who cost whom-ever he works for a pay-check from Mister House.
The Courier is contracted by the Mojave Express to deliver the package, and if you read the contract penalties it says: "Failure to deliver to the proper recipient may result in forfeiture of your advance and bonus, criminal charges, and/or pursuit by mercenary reclamation teams. Mojave Express is not responsible for any injury or loss of life you experience as a result of said reclamation efforts." So the main motivation for the Courier could be not having to spend the rest of his/her life looking over his/her shoulder for armed and deadly repo men.
Spot on, even if your Courier is not motivated by revenge, concerns over their future employment, need for cash, curiosity about why Benny did it etc (all of which are perfectly good reasons on their own), the fact is that if you don't deliver the chip you'll be hunted down for the rest of your life by mercenaries.
That's a result of your actions towards that faction, and is unrelated to Benny and the platinuim chip.
You simply have to kill off Benny, not for shooting you in the head but for his fashion crimes
It's funny, whenever I get to that moment where I can kill him, whatever character I'm playing with, I always get the same feeling - "all this trouble, all this chasing around the desert, and *this* is the guy? Is he even worth killing?"
I usually decide he is, though.
There a many reasons, revenge not being the least of them. Plus he was so smug you just have to put him in his place. Plus there's the curiosity of finding just what is going on and how circumstances led you to being shot in the face (did I mention revenge?), perhaps the desire to maintain your integrity as a courier by finishing the job (and thereby saving your own bacon).