John Baez, I refuse to say something is incorrect when I myself don't fully understand something.

>perhaps it's connected to the fact that I'm left-handed. This is dangerous for a category theorist!

It's a probably from a cultural bias. Westerners want really hard to see the number line as moving left to right, ie from their less dominant side to their more dominant side, probably precisely because it makes the \$$\leq\$$ operation easier for right-handed people to visualize.