This from Bum...
"Dream. Plan. Do."
This from RJM...
"Parents make kids go to school and do homework because its required. Parents limit snacks and activities for health reasons. But I don't understand how a parent can force a kid to participate in a certain extracurricular activity. It seems like a way to make him hate the activity."
This from the OP...
"I am trying to find that line between "encouraging" him to do the extra work to get better and letting him make his own decisions."
When our third and last kid clearly showed he was the ultra-competitive one that wanted to be an athlete, we certainly went through this struggle. Through trial and error 
, this is where we landed...
Frequently checked in and asked what his goals and dreams are. Regularly helped educate on how to work toward attaining those goals and dreams. Allow for them to change. Point out positive role models who have succeeded in accomplishing those same goals and dreams. Allow for "kids to be kids" and enjoy their primary sport/activity of choice as well as many others (And there were MANY others!). Give him a break when he needed a break. Steer him toward resources that will help him understand the effort necessary and the path to take. Realize that he won't always accept and utilize those resources. Support where/when needed. Back off where/when needed. Love him and enjoy where he's at regardless of whether his choices match what ours might be.
With video games, we allowed but set limits. With sports/extracurricular, we required that each kid participate in at least one of THEIR CHOICE for each season.
It really is a fine line and easier said than done.
As a coach, I've seen too many kids pushed too hard by parents and end up leaving or not enjoying the sport. But, on the flip side, many of the kids who continue to the next level had parents who pushed pretty hard. I would like to think that, in both instances, the driving factor was that the player had the dream.
As a parent, I believe we succeeded but not without our share of mistakes along the way. My measuring stick for our success... Cabbage is in his second year of college coming back from a lengthy injury that wiped out his first year. Last week, he commented that he really loves playing again.