No because he would be turning his back on his men.
Do you think Merritt Edson turned his back on his men when he resigned so he could publicly criticize Truman?
Under the right circumstances, Petraeus’ resignation could be the very spark that saves so many of his men. All three and four start generals are political - it’s part of the job. But, when the CINC insists on doing something monumentally stupid, it may become necessary for the general to stand aside in order to bring public scrutiny on the actions of the Pres__ent.
Generals serve the needs of the country first, and the needs of their troops second. The needs of their CINC, when they coincide with one of those two areas, can usually be handled as a matter of course.
But a CINC like Obama may have to be pushed aside, politically. The only leverage a high-profile General like Petraeus has is his resignation, when the Pres__ent insists it’s “his way or the highway” because “he won”.
Just my $.02, of course.