I think that's why people think of them as a couple. It's a common stigma/trope, especially in fiction, that old married couples are always bickering with each other, and in some eyes, that's what they see Ernie and Bert as: an old married couple that bicker all the time.
But really, this can be said of a lot of duos in fiction: Felix and Oscar, even Shredder and Krang (the latter of which, James Avery joked that he and Pat Fraley actually treated the dynamic of Shredder and Krang as if they really were an old married couple).