i'm not going to dissuade standing up to a bully. but the thing is that it doesn't work. telling kids they're being mean, when they're intentionally being mean, is actually just reinforcing them. it's rewarding negative behaviour with the attention that they're consciously seeking.
schoolyard bullying is all about establishing hierarchies - pecking orders. it's about establishing dominance and submission. i know it's natural for an adult to want to cuddle a child that's being teased, but it's the same basic twinge of empathy you get when you see a wolf pack fighting for dominance, or even a lion killing a zebra. it's very much a normal, cycle of life kind of thing. and, when you intervene like this you're just reinforcing the premise - that this child is an easy target, at the bottom of the hierarchy.
a better idea is to give the kid that's being bullied the tools to defend itself. in extreme cases, that it is legitimately going to require physical force. i used to get picked on when i was a kid because i was a scrawny, passive bookworm. i'd come home with bruises from being pushed around. my parents' reaction to this was to put me in karate - and i'll tell you that a few ninja moves did a lot to get some kids to back off, even if i never had to actually use it. and, in fact they teach you that when you take self-defense - it's never meant to be used, it's just meant to look scary. i'll acknowledge that i was maybe the exception in being smart enough to realize that at nine-ten years old and use it to my advantage. it didn't work in changing my attitudes towards things (i never got over my shyness enough to actually engage in any kind of sparring at the dojo, and i didn't keep up with it past the age of twelve - i really hated it), but sending me to these classes gave me an incredibly useful tool of intimidation when it was necessary. and, it was probably the only thing that ever could have worked because i remained an easy target.
in less extreme circumstances, like depicted here, the key is getting the kids to have the self-assurance to realize that what these kids say doesn't matter, or even to counter with comebacks.
the old cliche that you have to stand up to a bully is the flat truth of it.