I work in oil/gas consulting and our motto is that it's never a good time to go on holiday so just do it anyway! So long as not many people are on leave at the same time people's leave requests are always approved. It's just too hard to predict when it will be busy or quiet so we encourage people to go on their holidays and the rest of the team just cope without them.
As for having to take leave for a half an hour appointment! Insane. I can imagine in a law firm you do so much overtime anyway, seems so awful that they expect so much from their employees but give so little back