I don't think "SEC Pride" is fully appreciated by anyone except those who actually attended an SEC school, as opposed to just rooting for the team from one. It's about the fact that despite our obvious sports rivalries, there's sort of a brotherhood or mutual relatability among students and alumni of SEC schools that's attributable to the fact that the respective student bodies and the experience of attending one are almost identical.
With only a few exceptions, all SEC schools are "the" flagship public universities of southern states, with similar campus architecture due to being land-grant universities that were built around the same time, located in college towns with comparable atmospheres, and attended primarily by students who were typically in the (barely) second tier of top students in their high schools, second only to the handful of students at the very tippy-top that ended up going to Ivy League or other elite private schools.
I'm not aware of another athletic conference where the campuses, campus environments and student bodies are all so remarkably alike.