I face the same error while developing for the API 11. That was minimum of 14. But yes android studio never shows minimum then API 14. This is due to some Appcompat library.
Because when I dug out deeper then I found out that This Library was using minimum of 14 SDK. and due to manifest merging problem I think android studio is not showing minimum then that. At that time I was using 25.+ version of Appcompat library and I was using android studio 3.0.
You can find out more by selecting API 14 and then go into build.gradle file. now here you can change minSdkVersion to 11 or at any api level you want.
Then you can notice that while building you will get manifestMerger error with following proposed solutions
Error:Execution failed for task ':app:processDebugManifest'.
Manifest merger failed : uses-sdk:minSdkVersion 11 cannot be smaller than version 14 declared in library [com.android.support:appcompat-v7:26.1.0] \9fe0f18d3439e3d6185e96eddd3ec321\AndroidManifest.xml as the library might be using APIs not available in 11
Suggestion: use a compatible library with a minSdk of at most 11,
or increase this project's minSdk version to at least 14,
or use tools:overrideLibrary="android.support.v7.appcompat" to force usage (may lead to runtime failures)
So here is the problem and here you got the reason. May be some one can help you in bypassing it. I just thought to share my findings.