First and foremost, Danny is playing for $$$$. Missed games are missed opportunities for him to show teams that he is worth signing. Also, there's just a raw competitive aspect to it. Danny is a basketball player, and basketball players want to play. He hasn't played consistent competitive NBA basketball since May 2012, which has to absolutely kill him, as it would any pro athlete. He's seen the team enjoy tremendous success since then, and he obviously wants to be a big part of it. An athlete wants to get out there and play as soon as they feel they can. Clearly it seems like Granger feels like he can.
Vogel as the coach has to make sure that the most disciplined approach is taken. The team is winning a ton of games and Danny hasn't played in a while. Thus, from his perspective, there is no need to rush him back until he is without a doubt as close to 100% as he possibly can be. Vogel wants Granger to be contributing to this team in the Spring when the stakes are highest, so he doesn't want the team to do anything stupid by running him into the ground when they are able to win games without him. Vogel and the team have to make their decisions with the big picture in mind.
It's not surprising that their agendas might conflict a little. I don't think it's anything to worry about though.