I think you don't ever really push -- except if the kid isn't living up to his part of the basic bargain. You find a way to enable what's inside the kid to develop and flourish.
I'll give you an example. When my guy first started playing baseball, he was really truly indifferent to it. He was one of those kids in the first couple of years in little league who would pick flowers in the outfield. Nobody wanted to play catch with him during practice cause he would be making goofy throws all over the place, and wouldn't take throwing drills seriously. As he matured, he became a little more focused but was still not really into it -- though his pure athleticism gradually became harder and harder to miss.
First turning point came when he was 11, I was assistant coach to a really amazingly good coach, who helped the kid see that he could actually be good at this game if he worked at it. Thanks to that coach, his interest in the game perked up. He joined a travel team -- not the most talented team -- but one coached by a mensch of a guy, who really believed in him and gave him lots of opportunities to succeed -- which the kid mostly did. As a result he became much more into the game.. He actually started working hard to get better at the game.
I'm not saying it went swimmingly from there. Come freshman year in HS, for example, he was cut (in favor of certain lesser players who are long gone by now, but played travel with the then JV coach). I thought he'd be crushed -- he was -- but the thing that took me by surprise is that he was completely unwilling to give up on what had become his dream buy then. He went on to work like a fiend with a personal trainer/coach who helped him take his conditioning and his game to another level. (He was also fortunate that he could keep playing that year, since he was just 14 and played all season long with a 14U team full of 8th graders and other frosh rejects who wanted to keep at it.) All I did was pay the bill and keep encouraging him to believe in himself and work at getting better. It taught me a lot about him. From an indifferent little leaguer he had involved into a young man with burning desire and complete determination all coming from someplace inside of him. I think if I had "pushed" he would have resented me and pushed back and his own internal drive would have never taken over.
On the other hand, if I had just stood by and let the JV's coaches assessment be the last word, that would have been a mistake of a different kind. Instead of enabling him, I would have been partly responsible for disabling him. So I think I did my part not by using but by believing in him and being will to pay for a personal trainer/coach that could help him do the actual work it took to keep his dream alive.
By the way, the then JV coach who cut the kid and kept others that fizzled out quickly has long since admitted he made a mistake in cutting the kid. In fact, my son is playing for his travel team now. He and that coach have a great relationship; he is one of the kid's biggest supporters. Irony of ironies.
Of course the kid never lets the coach forget what a mistake he made. Hit a grand slam the other day and he said to the coach "And you cut this bat? Don't you feel silly? " They had a good laugh over that.