The fact that money from the shirts/poppy symbol is going to support a military body is enough for FIFA to say, "Like f***". They can't afford to set a precedent. It's nowt to do with international football which is what this boils down to. Sometimes matches occur that are played in politically-charged circumstances: matches with Israel, the Koreas, some African games, etc. FIFA has to ensure that ultimately the game is simply a match between two football sides.
I know people like to lay the boot into FIFA because they're a bunch of corrupt wankers, but their job is to run football and they're doing the right thing in this instance.
How on earth is the poppy going to cause unrest amongst rival nations? It stands for nothing but respect and remembrance.
It sets a dangerous precedent. You allow this and then you have countries wanting to commemorate war victories or pay respect to charities or all kinds of nonsense. Putting a blanket ban in place (which has always been the rule) means this doesn't even become a topic. Like Keefaz says it's a sport and FIFA's responsibility is to make sure it remains solely about the sport. It's their job to make sure politics and sport remain separate, and I completely agree with that.