I think that this case is simpler tbh: Taemin is narcissistic (remember, he recently said he loves being worshipped as a god), he is also clearly not into ideals such as serving his country, so for him enlisting is clearly lost time. He is obsessed with age and by the time he will be discharged he will be 30 (not a problem imo, but for him clearly it is).
Also the Korean military is strict, he cant act like the maknae baby, he has to do what he is told, eat what they give him, no constant spam on socials, coexist with strangers... lots of stress for him.
Narcissists throw tantrums when they can't have their way.
Remember this live? Taemin supposedly did not have time to change. I call BS: how much time do you need to put on normal pants and a shirt? Nope, he has to be in the spot light.
Great example for his fans.