iserith
Magic Wordsmith
I don't see anything in the spell description that implies in the slightest that the movement is set in a single direction. And what is written clearly lists that it moves away from the caster at the start of your turn, not away from the point of casting.
Agreed on the reading.
As a matter of fact, if I cast the spell and a DM surprised me with the ruling that it moves away from the point of casting as opposed to me, I would argue with them.
While I would personally not choose to argue with the DM, I'm all for players pointing out to me where I have something wrong as DM if it actually matters to the outcome of the situation or to their pending decisions. I don't have every spell detail memorized. If I as DM get something minor wrong that has no appreciable impact on the current situation though, man, I prefer such niggling details be saved for a break. Whether or not this reading of cloudkill qualifies as important or unimportant depends on the situation in my view.