Canucks are a deep team. Lots of competition. You gotta earn your ice time. If you're not playing hard enough or well enough for what ever reason another player that is playing well will get more ice..
Almost everyone has sick family members. Or dead family members. No need to over analyze his father being sick. That's part of life.. not just for hockey players but everyone in general.
When Boeser plays better Green will reward him with more toi.