Today my horse took off with someone?

[Bec]

I agree with the other answers- chances are FB wasn't as experienced and obviously horses pick up on that. It doesn't sound like your horse was deliberatly naughty (I mean she could have bolted with him at any point if she sensed him being inexperienced or unbalanced). What probably happened is she wanted to join in the canter, FB chickened out but then accidently gave an aid (leaning forward, gripping with legs, "shuffled" with his seat)
It's hard to recreate it - you don't know what accidental aid FB might have given, you don't know how his nerves were etc.
It could also be weather related - as others have said. Spring is coming. This change can make some horses play up more (just being more active). She could have spooked at something - or napped/spooked (you know how some horses suddenly decide the gate post is the scariest thing in the world despite walking past it hundreds of times)