I have something but it may take some time to work out. Bear with me. The first clue to this riddle is the three-word phrase "my old man." We all know that "my old lady" is slang for my wife. Therefore it stands to reason that my old man, would be a husband, and due to the current political climate, it's likely a straight woman referring to her male spouse, also presumably straight. The genius of the riddle lies in the last two words, because after all, any jackass can figure out the first bit.
" . . . holds pencils." The sheer simplicity of it is it's brilliance! It is self-evident, it means exactly that, yet it does not! Aha! What are we, the faithful Quiznos patron, to glean from this conundrum? I shall tell you. One holding a pencil is likely doing some form of work. Perhaps figuring out a mathematical equation, perhaps balancing payroll, creating artwork etc. but it seems that there is some evidence of productivity. And productivity, ergo, yields results, vis a vis financial stability. Holding a pencil is working; holding pencils is providing.
So isn't the writer actually making an observation that in this modern day and age, post-19th Amendment, men are still the financial rock of the family unit? We have come so far, yet have we gotten anywhere? This is the distilled essence of our Quiznos author.
This is someone's answer on what it could mean.