I know it’s damn near impossible to pinpoint when exactly people started saying that, but does anyone at least know why we say it? Are molasses slow?
Molasses is a thick sugary liquid. It pours slowly. That’s about it, really.
Molasses is a thick, syrupy byproduct of the sugar-manufacturing (from sugarcane) process. If poured, it flows very slowly. If you don’t believe me, go to the store, buy a jug of molasses, and sit at your kitchen table holding the bottle upended over a bowl until the entire thing is empty.
And then you can make rum!
Thanks. I’ve eaten foods that had molasses in them, but never saw the stuff on its own, so I didn’t know it was a thick liquid.
My versian, via American (Montana) grandmother is
“Slower than molassas in January.”
I used to love sneaking a spoonfull of the stuff out of the carton. 
Slower than molasses running uphill on a cold January morning.
Slower than molasses running to school barefoot in the snow uphill both ways on a cold January morning and you’ll never see molasses these days doing that now will you with their new-fangled game boys and such.
However, a flood of molasses can flow fast enough to drown 21 people. In January, no less.
Ah, yes. The Great Boston Molasses Flood of 1919.
My favorite expression along these lines has always been “slower than sucking peanutbutter through a straw.”