I've mentioned this before, and I expect others remember the details better than I, but the real turning point for Tech football was Sputnik. The country panicked when the Russians beat us to space. We had NO idea that the USSR was even competitive with us in science and technology: we thought they just stole from us (the "A"-bomb, the"H"-bomb). so when the first satellite went up, the nation was galvanized. Tech IMMEDIATELY began to talk "de-emphasizing" football, and it was downhill from there. (Our last gasp, the '65 team starring the young left-hander, was known to real Tech fans to be winning almost sheerly on will, we had no business going undefeated nearly all year.)
Everybody panicked, particularly about math, and how US school kids did not know any, after Sputnik, and schools like GT really had no choice but to push football back and focus on academics. meanwhile Ole Miss and bama,etc, were spending huge amounts of energy on cultural "conservatism" (read: segregation), and football fit that attitude.
Anyway, Tech grew in various very positive ways, and by the mid-60's simply was no longer an SEC fit. When we went indie, the program really suffered. UGAg had the highly organized, highly professional young Dooley for a coach, and they just took over state football. The fact that Dooley had the only decent program in GA, SC, and Fla, and still couldn't dominate like Bear was doing, or like Dodd did in the early to mid-50's, shows that he had much bigger limitations than the doggies will admit, but he beat us.
That's my rant, and the end of my two-fingered typing patience. Maybe it adds a little perspective to why we left the SEC.