This also isn't about picking a fight with a raider. If I had to approach one of my raiders about something they could do in their rotation that would give them free dps, I'd just do it. I'd be friendly about it. I'd just put it out on the table, 'hey, here's this thing you can do that is definitely totally free dps and doesn't even require you to change your rotation (remember, you just replace glaive toss with arcane shot whenever it's up, super easy). You should do this thing because we all love killing bosses and killing bosses is cool.' BAM. No fight picked, argument made, free DPS gained.
Being a raid leader is also about being very diplomatic with your raiders and knowing how to get them to perform better. You're focusing way too hard on the babysitting aspect of it. Raid leading should only be like babysitting if your raiders are babies. And hey, sometimes they are, but I'm going to go out on a limb and assume that this guy is perhaps mature enough that if approached in a proper and friendly manner he won't flip a table and throw a temper tantrum.