I know a lot of schools have some quirks, traditions, etc. that seem odd from the outside but I've never seen anything as consistently weird and culty as Texas A&M.
I think it is the product of two things. 1) being from Texas and 2) a stereotypical little brother complex.
Im a big advocate of healthy state pride. Texans seem to take it to extreme levels, which is harmless but can be very bizarre to observe from the outside.
Its no secret most state flagships historically are the more successful school relative to their land grant brothers (if the land grant is a separate school). Accordingly, you'll find some weird songs and traditions at said land grants where it is explicitly about their hate of the flagship university. Im intimately familiar with this, every first down at North Dakota State elicits a "Sioux Suck Shit" from the student section no matter the opponent.
Texas A&M similarly falls victim to being Jan Brady, they just do it bigger and better than everyone else. Its really no wonder David Koresh chose Texas as his base of operations, the people there are very susceptible to this sort of thing.