We recently started learning about pericyclic reactions and this is a step from a mechanism I'm working on for an assignment. I believe that the arrows on the right are better than the arrows on the left because if I throw in some charges instead of arrows, the outcome I get on the right is somewhat more "stable?" for the reasons stated on the picture. Am I correct in my assumption? On the overall reaction, it's the 6 to 7 step that I'm interested in.
The answer is rather bland and probably not what you want to hear. Electrocyclic reactions are called electrocyclic because they are cyclic. (Please don’t see
cyclic circular reasoning in there.) They proceed in a cyclic, i.e. fully symmetric fashion. You simply cannot draw one arrow direction and claim it is the most logical or the only one possible. You could draw these arrows as you drew them, but you could also formulate a radical-based mechanism (each double bond splits into two radicals which combine with the two of the other double bond) at no loss.
Thus, there is no way to say whether left or right. The reaction happens; in a cyclic fashion.