The qualifications to become a Director really just amount to, well, doing it. And doing it halfway decently. If you can prove yourself then you might be able to get in.
There's a fair amount of luck involved with anything related to the entertainment industry. The old maxim "It's not what you know, it's who you know" should be tattooed on your forehead if you want to break into movies. If you're good, and if you can meet the right people, and if they believe you’re good, then you may get a shot.
The focus on networking is one of the big perks that comes from film school. Not only do you meet other students who will (hopefully) work in the industry one day, you may get to meet alumni who are already working. Some of the best film schools (like NYU) also offer internships with Directors. Sure, you'll probably just be fetching them coffee, but fetching Martin Scorsese coffee between shots will open a lot more doors than working at a Used DVD store.