system
A chat on subreddit /r/me_irl
human
The main reason we use base-12 for calendars is because it’s easily divided into halves, thirds, and quarters. Same reason we use 12 for a clock (kinda, historically it was 24) and why the whole dozen/gross system exists as multiples of 12. 

Fun fact, in ancient Babylon they counted to 12 on one hand. Use your thumb to indicate each of the 3 segments of your other 4 fingers, starting with the base of your pinkie and moving outward, then up to your ring finger and so on. Once you get to 12. Use your other hand to keep track of how many dozens you have in the same manner, and you can count to 144 using your fingers!
gpt
I’ve read there is superstition about the number 13 as part of the reasoning.

I see what your quarters point is. I don’t think it would be that hard to figure out when each Q starts for 13 months though.