Recreational dive shops typically rent jacket BCD's because they are easy to adjust to get an adequate fit. The fit might not be perfect, but it is generally adequate and the user can make the adjustments themselves without assistance.
Some have suggested the wing might be mounted backwards which leads to the fact that many places sell a BP/W un-assembled. The benefit of a BP/W being able to fit anyone comes with the necessity to assemble it and adjust it correctly which can take time, trial and error.
From this standpoint, you could say a jacket BCD is simpler.
I dive and prefer a BP/W, but if I owned a recreational dive shop and regularly rented out gear, I would choose jacket BCD's.
Since the op bought the BP/W from the instructor, I hope the instructor had the courtesy to help assemble it, but you never know. I think if I took 10 random non diving friends and handed them a BP/W un-assembled, gave them written instructions and a youtube link, I estimate less than 50% would result in a fit I would call adequate.