According to this my max trailer weight without a 5th wheel is 12,500 and with a 5th wheel it drops to 10,600. Why is that?
No one knows why a truck makers assigns ratings to a particular truck. Its been this was since mfg started assigning numbers to their trucks. RV folks like to guess and some guesses get pretty wild.
However we do know a 5th wheel trailer places all the hitch weight (pin weight)..plus the weight of the hitch itself over the trucks rear axle. That model F250 has either a 6084 or 6100 RAWR. These year model F250 rear axle can weigh in the 2900-3000 lb range leaving around 3000-3200 lb for a in the bed payload.
You have the truck so drop by a set of CAT scale and get your trucks front and rear axle weights. These are the numbers that will tell you what the truck can safely handle in all situations.
The RAWR includes rear axle assy....tires....wheels...brakes....rear spring pack.
Now if your F250 has the heavy service package or camper package the front and rear brakes...suspension is upgraded two times. Same as a F350srw GAWR packages.