My understanding is that Outlook for iOS uses a cloud service that talks to the Exchange server and stores your credentials/data: https://blog.winkelmeyer.com/2015/01/warning-microsofts-outl.... So logging in involves giving Microsoft (and indirectly Amazon, since it runs on AWS), clear-text access to your information.
My Exchange server is 15 feet down the hall. When I use a normal Exchange client, the only people who can see my data in clear-text are myself and my employer (who owns the Exchange server). Anyone in-between just sees an encrypted stream. But when I use Outlook for iOS, people I've never met at Amazon and Microsoft can see my email.
I think the former situation creates a legitimate expectation of privacy. I think the latter situation does not. Which is why I use Apple Mail instead of Outlook for iOS.