You could say 'Football is played all over the world' (everywhere). To descrbe popularity, then the first sentence is the one to go for. It is possible to use sentence 2 but it has a different meaning- it would mean that it is the number one sport in every part of the world, which it isn't, as opposed to just the sport that is, in total, the most popular. It would make no sense to say that 'Mount Everest is the highest mountain all over the world', so in most cases your teacher is right.
