The custom of praying mincha twice a day

Rambam mentions a curious minhag (mt hilchos tefilah 3:3) of folks praying two mincha services, one by mincha gedolah and the other at mincha ktana (one as a chova and the other as a reshus). Cohering with his opinion in the previous halacha of mincha ktana being the ideal time for the afternoon prayer, he agrees with the gaonim who cautioned people to make the earlier one the optional prayer (interesting that one can designate a tefilah as a reshus even before praying the obligatory one). 

How and why would such a peculiar custom develop?

Perhaps it sprang up amongst jews that lived in predominantly muslim populated lands. Muslims pray 5 times a day. 2 of them are afternoon prayers, one in the early afternoon (dhur) and one later on in the afternoon (asr). Not wanting to appear any less devout than their muslim neighbors jews may have figured out a way to get in an additional prayer, thus starting the strange minhag of two minchas daily!

What is fascinating is that initially Islam had two prayers daily, it only got bumped up to 3 after Muhammad emigrated to Yathrib (what came to be known as Medina) and first met Jews, was impressed with them, and borrowed a whole bunch from Judaism (eg kosher and yom kippur), 3 daily prayers included. 

(When he saw that the Jews weren't buying what he had to offer he disassociated from Judaism, changing the direction of prayer from Jerusalem to Mecca in addition to other things) 

The Koran only mentions 3 prayers which mimic the Jewish ones. 

Perhaps two more were added over the years in an attempt to outdo us with Jews eventually trying to play catch up.

Interestingly, on Yom kippur, when we have musaf and neilah, in addition to the regular three, we actually do hit 5.