I see that 12 lb flouoro is popular for a football jig, while 15 lb flouoro is popular for a carolina rig mainline. So with that, why do people recommend throwing them on the same rod?

Use the 15#...that's the line on my main jig-rig.

Because the rod has a 10#-20# line rating.

Both those lines seem a little light for me.   In the lakes that I fish in Missouri, I don't throw any kind of jig on less than 15 lb fluorocarbon.  I don't throw the Carolina rig all that much, but when I do I have a 7' MH spinning rig that I'll throw 20 or 30 lb braid with.  With the Carolina rig, I get longer casts, better feel and better hook sets with the  MH spinning gear.

What same rod are they recommending?

 

I prefer a heavier MH for jigs and a true H for Carolina rigs.

2 hours ago, johnsmith said:

I see that 12 lb flouoro is popular for a football jig, while 15 lb flouoro is popular for a carolina rig mainline. So with that, why do people recommend throwing them on the same rod?

I wouldn’t pay much attention to individual opinions unless you know the application of their recommendations (dragging over pea gravel is different than dragging over heavy chunk rock).  Line choice is going to be influenced by the structure/cover you are fishing and that applies whether it’s a football head or Carolina or anything else.  I have 3 dedicated bottom contact baitcasters to cover all situations so they have to serve duel purposes.

I personally like 20# fluoro  mainline on the ol ball and chain 

It can handle more abrasion and the hookset is better 

I like braid mainline for C rigs and 15lb fluoro for football jigs. 

Because with a Carolina rig traditionally youre throwing a half ounce weight connected to the main line and then usually a lighter line on the second part after the swivel. A football jig or any jig is just connected to the main line. With a Carolina rig you can throw a half ounce but you can throw a light liter like a 10 or 8 pound to get more of a finesse presentation of you like! I use this in Cali 

Carolina rig 7'6" Heavy F or XF 40lb braid to 15lb.ish copoly - sometimes just 20lb fluoro to the copoly but I prefer the braid.  I get better hooksets. 

Football Jig 7'4" 30lb braid to 15-20lb fluoro leader

 

Good starting point and then you can adjust your line and rod to the conditions you are faced with. 

Popular where? I use 15 or 20 lb fluoro on a MH or H rod for jigs and 40 lb braid to leader on a H rod for C rigs.

10 hours ago, johnsmith said:

I see that 12 lb flouoro is popular for a football jig, while 15 lb flouoro is popular for a carolina rig mainline. So with that, why do people recommend throwing them on the same rod?

I’ll answer your question a different way.  The reason you can throw them on the same rod is because the qualities you look for in a rod apply to both techniques.  I use an NRX 873 CRR for Carolina rigs but it is also an outstanding jig rod.

20 hours ago, johnsmith said:

I see that 12 lb flouoro is popular for a football jig, while 15 lb flouoro is popular for a carolina rig mainline. So with that, why do people recommend throwing them on the same rod?

Guess I am obtuse.  Clueless?  Slow?  Imperceptive? Dense?  Dumb?  Thick?  Slow on the uptake?  Uncomprehending?  But all I got out of this is that the OP is wondering why someone would suggest using 12# and 15# on the same rod.  He doesn't ask what are good rods for these techniques?  What power is best?  What line is best?  What color is best?  What weight is best?  Etc.  Etc.

On 3/25/2021 at 10:45 AM, johnsmith said:

I see that 12 lb flouoro is popular for a football jig, while 15 lb flouoro is popular for a carolina rig mainline. So with that, why do people recommend throwing them on the same rod?

Could be that people are recommending the same rod for both applications, but not the same line which would to me imply that you would probably want 2 of that particular rod if you wanted to do both at the same time. Example: "Rod XYZ is a great rod for Carolina rigs when spooled with 15 flouro and is equally adept at throwing football jigs if spooled with 12lb Flouro."

 

I would simply read into that s saying that it is a sensitive rod for bottom applications that has enough backbone to set the hook at a distance.