application sandboxing in iOS, which restricts applications to just their individually allocated areas on the filesystem (and prevents access to any other application's or the OS' files as well as memory, network communication, etc.), an app written to be like an antivirus cannot really read anything outside of its own sandbox.
Due to limited multitasking in iOS, an app written to be like an antivirus cannot really run in the background for a long time to scan the system continuously.
Both these factors together make it impossible to make an antivirus like app for iOS unless the device is jailbroken.
Any antivirus, if at all deemed necessary, would have to be made by Apple. Third party app developers are limited to the restrictions mentioned above.
Further to the comments on the question, it may be worth one's while to look at this presentation titled "The Android vs. Apple iOS Security Showdown - July 2012" (especially slides #20 through #33).