Seems like that might be kind of a myth. There’s a lot of sites that claim that, otoh here’s a Quora post saying the opposite:

Benjamin Franklin was on the Committee of Five, along with Jefferson, that drafted the Declaration. And the reason why there was a committee assigned to write the Declaration was for no more boring a reason than that’s just how parliamentary procedure works. Expressing the sense of Congress is rarely, if ever, left up to an individual, no matter how revered.

But the primary reason why Jefferson was chosen to draft the Declaration over the other members was because he held greater political standing as a Virginian than John Adams (also on the committee) being from Massachusetts, and Benjamin Franklin was mostly preoccupied with the Committee of Secret Correspondence’s work of finding allies for the war effort.

Not to say that Jefferson’s writing ability wasn’t a factor in his selection over the other two members of the committee; but he was actually reluctant to take up the task, being otherwise a reserved person and inexperienced politician.