iPhone, iMac calendars won't sync

You have omitted the most key piece of information ...

Where are your calendar(s) stored? They are likely stored in different places.

On the Mac, in the Calendar app, click the "Calendar" button in the upper left to display the calendar(s) you are using.

On the iPhone, in the Calendar app, click "Calendars" at the bottom center.

On the phone

Log out of Find iPhone

Log out of iCloud

Do a forced restart - After shutting down all open apps using the app switcher - invoked by quick double press of the home button and swiping up on each app till it flies off the screen.

Hold the sleep/wake and home buttons down together till you see  logo - then release and allow normal boot up

Then sign back in to all of the above

I guess you have personal reasons not to use iCloud. To me, the iCloud solution seems like the natural answer because changes made on one Apple device appear immediately on all others.

Anyway, for local calendars, see this article:

Sync your iPhone, iPad, or iPod touch with iTunes using USB - Apple Support

When you sync, check the "Info" tab to make sure the sync instructions are set up correctly. As I say, I use iCloud so I can't be of much help because the "Info" tab in my case simply says iCloud is used to sync calendars (and notes, etc.).