Apple does not allow external SD cards because if users were able to use external Sd cards, user will see it as an opportunity to put data into the phone. Data, here is mostly going to be apps, music and movies which will affect the use of iTunes and iCloud. Apple's strategy is to keep its uses glued to what has been provided by the operating system. If apple makes SD card slots it will lose a lot from its money making resources.
Allowing the use of external SD card will might affect their operating system and devices. If Apple decides to allow SD card on their devices it would be difficult for them to go into the market because it does not produce SD cards, in order to avoid the competition, they do not have an SD slots.
In summary, Apple does not allow external SD card because of some financial reasons, it is avoiding competition and also protecting its operating system.