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.
There are several reasons why Apple does not allow for external SD cards. The main reason is that Apple does not want the competition. This means that if they put a SD slot in say an iPhone, this would allow for a person to use an SD card that could have things on it such as music. Apple has iTunes which allows for users to have online access to music and be able to download it directly to their mobile device or personal computer. Apple does not make SD cards so it would be impossible for them to delve into that market. Another reason that Apple does not have external SD cards or SD slots on their devices is that they believe that it could comprimise their operating systems and devices. Apple is known to sell data to its consumeers. If there were an SD slot, data from the SD card and from outside services would be put into the device and it would also be able to be accessed by other people. One can easily say that the reason that Apple has not allowed external SD cards and SD slots is financial reasons and not wanting any outside direct competiton.