I have been at this board for almost 11 years (I had lurked some years before), but this question makes me feel like a noob. The Pit, I understand. But what stands BBQ for? Surely not grilling?
For flaming people and things.
adds more lighter fluid to glowing coals
You’ve heard of “flaming” people? Here it’s done n the BBQ Pit.
Burn, baby, burn. 
Barbeque (also spelled barbecue). Standard shorthand in the US for cooking over hot coals, which traditionally might be placed in a pit in the ground.
I knew what BBQ is in real life, but I hadn’t thought about flaming (as in burning) people! You’re all sadists!
Negative comments about us should go in the Pit. 
How is “sadists” negative?
I’ve always thought of it as “We so badass, we flaming people”… but to be honest, it’s not that bad in the Pit. So “grilling” is more appropriate.
Back in the early days of the internet, when two people or more got into an out of control argument/rage-fest it was called a flame war. The term seems to have dropped out of use, but that’s the origin of the BBQ pit name. A place where people could have flame wars.
It implies we’re all wimps. Otherwise we’d be sado-masochists. 
It’s a cookbook!
How to Serve Straight Dopers?
I always took the forum name to mean “roasting people,” as in hurling invective at them.
Just to put things beyond the Valley of the Shadow of Doubt:
flame (noun)
6 : an angry, hostile, or abusive electronic message
flame (verb)
2 a : to burst or break out violently or passionately flaming with indignation
b : to send an angry, hostile, or abusive electronic message
Indeed, Wikipedia has a whole article on Flaming.
And the SDMB used to have its own unofficial “Page O’ Flames.”