Training
Any reasonable 22nd century civilization is going to have robots that can inspect the hull. All you need is a camera on a robot arm, a space-traveling selfie stick (this was done on the real-world space shuttle after the Columbia disaster). But the civilization doesn't have robots that can handle every possible occurrence. If you had those robots, you wouldn't need a crew.
So there have to be some things that the robots can't handle. Probably not simple inspection, but repairs, upgrades, maintenance, sure. This seems to be a pretty small ship, so there's just not room for lots of robots. Humans are and always will be generalists, but maybe even 22nd century robots are specialists, like most present-day robots. For almost any given task, a robot will be better than a human - but only at that specific task. And this ship might just not have the room to carry dozens or hundreds of specialized robots.
Before a human can be good at any particular task, they have to practice. 500
Real-world astronauts (and pilots, doctors, soldiers, nuclear power inspectors...) train extensively before they go on the job - but that's not an option if your ship is spending years on a journey. Naturally the crew will train before they leave, but they still need to practice, and they'll probably cross-train each other in case somebody dies along the way.
But since the ship is too small to carry lots of robots, it's too small for extensive training simulators. They'll do what they can with their VR goggles, but it's just not the same. Before any crew member can be considered qualified, and periodically every so often afterward, they have to actually perform the tasks in question. And if those tasks are hull repair, engine maintenance, asteroid prospecting, or whatever else they do on their spacewalks, then sometimes you've just got to go do it.
But make no mistake that they would definitely keep this to a minimum. The hazards of spaceflight - especially at interstellar speeds - are tremendous. You'd likely have to carry a huge inflatable debris shield - basically a space umbrella - in case you get hit by a speck of dust. Radiation would limit the circumstances and the duration of your spacewalks. Space is not an environment conducive to human life. 500