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iPhones do not currently support push email, except through iCloud or Microsoft Exchange. iCloud email is not designed for business, and while Exchange email is, many are using alternatives to Microsoft's email system. This poses businesses a problem, as IMAP email is 'fetched' from the server at scheduled times rather than pushed directly to the device, meaning critical emails could be downloaded five or ten minutes after it was sent.
But the reason why BlackBerry devices offer push-email is because Research in Motion offers an email service that fetches your email from the server, like Google or Yahoo, and 'pushes' the email to your smartphone. Apple would have to invest millions of dollars in providing such a service for IMAP users, and frankly, the incentive just isn't there.
Image source: Apple.