Calendar won't let me add new events on my iPhone
I had the same problem, went into the calendar, tapped on "Calendars" in the bottom center, here there were two calendars listed - holidays, and birthdays.  I pulled down on these items (like scrolling, the screen refreshed then showed 5 calendars.  From some reason I-cloud was not selected, I selected this and all the calendars listed became active.

I went back to the calendar view (by month) and am now able to add events.

BTW, none of the other options I have tried worked, only this method.  Under general settings both my iCloud and Yahoo calendars were active, but under the actual program they were not.  Don't waste your time in the general settings change it from the program.