What makes FRC a sport?

[Jon Stratis]

Collins English Dictionary - Complete & Unabridged 10th Edition Defines Sport as:

1. an individual or group activity pursued for exercise or pleasure, often involving the testing of physical capabilities and taking the form of a competitive game such as football, tennis, etc

Lets break it down piece by piece:
an individual or group activity I don't think anyone will argue this.
pursued for exercise or pleasure I don't know about your team, but our team has fun, and derives pleasure from seeing the robot compete.
often involving the testing of physical capabilities and taking the form of a competitive game The basic structure of FIRST competitions is a competitive game. Further, it is a test of physical capabilities - of the robot, not the student.

It's a question of how you define the competitor in the activity. If your friend has any doubts that your robot is a fierce competitor that requires all the athleticism and endurance he thinks of in sports, first show him a video of a hard-hitting match. Then tell him he can stand in for one of the robots, and you'll have paramedics standing by to reattach his severed limbs when he's done