The OP specifically asked about lenses suitable for photographing schoolchildren for a school. He showed a sample of his animal portraiture. And then after some standard recommendations were made, we get a stream of photographs from posters using all kinds of other lenses, in an attempt to demonstrate that such recommendations were narrow and that a portrait could be shot with whatever lens one feels like using, which of course completely misses the point.
Did you actually SEE the photo the OP posted? Fantastic photo of a ram. Beautiful detail, rich tones, and of impeccable aesthetic quality. I can totally understand how a school could see that kind of work and say, "I want him to photograph our students."
Having looked at that picture of the ram, I'd now ask what makes that picture ? A pleasing portrait indeed but it is about the subject, the lighting and the post processing, not necessarily in that order. The subtle nuances between lenses is, in the case of this portrait, irrelevant.
The OP says he already has the 70-200/2.8 IS, and I'm not an expert on the subtleties of a ram's nose proportions, but that picture could easily have been taken on a 70-200 f4, never mind a 2.8. There is no indication of where the background is or how far away the photographer was able to be from the subject, so without looking at the exif there is no way of saying.
As others have pointed out, how the subject responds to the camera is much more important, and in the case of this ram portrait I don't see much interaction; it's the lighting and the post processing.