My theory for why "San Fran" is looked down upon is that the person saying it is perceived as making a claim to status: 'I am so cool and hip that I am on familiar terms with "San Fran".'

But shortening San Francisco to San Fran is both very obvious, and betrays a cheap attempt at sophistication that the soul of SF rejects.

SF feels like a transitory city as multiple successive waves of people drift in and out. That also contribute to why a shibboleth like this gets a lot of airtime. The episode probably recurs weekly in bars all over the city as someone who's just moved here calls it "San Fran", only to be corrected by someone who's been here for just a little longer.