Two worlds simply.
There is the conquest 1vs1 crowd that gets all the support from EUGEN. Toxic at best, I find no other words for those guys. They are labelling themselves already, no need for me to do it really.
Conquest Team games (3vs3/4vs4):
more enjoyable, nice people there, too. But very tense games and somehow they never seem to be really decided once they are over. I played that for a while and also successful, but it never was my favourite mode because it didnt really feel like war.
in 10vs10 conquest just does not work really.
Timed Destruction:
The abyss of wargame and most certainly even worse than 1vs1 conquest.
Usually pubstompers with Atacms just waiting for some fools to step into the trap.
30-40 mins to achieve a certain amount of points.
The games resort to arty camping and a lot of plane spam, while the ground battle evolves into the "sitzkrieg".
10vs10 Destruction:
People who just like to have a good brawl. Usually people who like to fullfill certain roles like artillery, air support or frontline brawler.
Very dense battles with a lot of fighting going on nonstop. Really fun for teams and the only mode where even the "losing" side can have real fun by making the winners bleed dearly.
Sadly, due to the bad design of maps and the too big 10vs10 maps, this mode is now only possible on 4vs4 mapsize really.
The rest is just minor modes, like Total Destruction/No Time Limit, my prefered mode because it rewards resource oriented play and punishes spammers.
As for your question:
People dislike destruction primarily because of "Timed Destruction" or because they consider themselves to be an eSports Elite

(toxic etc.)
EDIT: as if it was a claim for the legitimacy of posts: I have a combined 4000 hours in 3 Wargame titles lol (and still a life, surprise!)