There might be a story idea in the "fact" that the middle of the year is not the moment when June 30th becomes July 1. That is when the seventh month of twelve begins. But most of the time there are 365 days in a year. That means the 183rd day is the midpoint of the year. (182 days times two is 364.) But thanks to the Romans who gave us most of the calendar we use February only has 28 days. Julius and Augustus Caesar decided their months, July and August, would be at least as large as any other month, and the days disappeared from February. Which was the last month in the Latin Calendar, the year started in March. Notice September is related to the Latin for 7, October to 8, November to 9 and December to 10.
So the 183rd day in 2018 AD (in Latin, anno domini, the year of the lord) is July 2nd. I submit for your consideration at noon on July 2nd the year is half over, and half remains to come. If you think the year is half over now, if you are reading this July 1, 2018, wait until noon July 2nd to celebrate.
I am not sure how this might make a story, but it didn't seem to fit anywhere else. Maybe time travelers get somewhere later than they expected because they asked to go half a year?