The actual distribution in developed countries is not uniform: there is a spike at the end of September (because many more people make babies at or around New Year's Eve) and a considerable drop on Dec. 25th (because people will avoid that date and provoque the birth some days before in case it might happen).
Also, on the site there is a huge spike on Nov. 15 which, incidentally, is the birthday of the author: maybe they tested it many times?
This is a nice story I've heard many times, but is it actually true? Like what are your statistical sources here?
https://github.com/fivethirtyeight/data/tree/master/births
For the period 2000-2014 the number of births by month, divided by the number of days in a month, is:
1 31 5 072 588 163 631.87
2 28 4 725 693 168 774.75
3 31 5 172 961 166 869.71
4 30 4 960 750 165 358.33
5 31 5 195 445 167 595.00
6 30 5 163 360 172 112.00
7 31 5 450 418 175 819.94
8 31 5 540 170 178 715.16
9 30 5 399 592 179 986.40
10 31 5 302 865 171 060.16
11 30 5 008 750 166 958.33
12 31 5 194 432 167 562.32
365 62 187 024 170 375.41
Edit: also, here, a graph per day:
https://www.reddit.com/media?url=https%3A%2F%2Fi.redd.it%2Fm...
(The source is mentioned but I did not verify it directly).
Bottom line: hospitals are short staffed on Xmas so they set scheduled procedures which may induce labor for the day before or the day after whenever possible which preserves their limited capacity on Xmas for unscheduled births and emergencies.