CORRECT! There is absolutely, positively no reason why the average user would want to use anything other than iOS or Android on their phone -- you just can't compete with literally billions of dollars spent on perfecting the user experience in both operating systems.

So, you pick away at the places where Apple and Google choose not to compete. In particular, both companies drop support for older devices very, very quickly; there are certainly innumerable devices out there sitting in drawers or on shelves because they're considered out of date. Target these machines: make them useful for some other purpose, be it games, or media servers, or even just simple remote controls . Allow people to make use of hardware for new purposes, instead of as their phone.

I don't think you can really compete with iOS or Android by coming out with an OS that serves the same purpose as iOS or Android. Serve a different purpose, though, and folks may find an interest...