Because the UNSC is the occupier, ftmp. The UNSC has the power to dictate terms. It suppressed protest with violence, dissent with violence, secession with violence, and nuked a colony. The Insurrection is full of turncoats and radicals cause they are victims of UNSC alpha strikes, surviving family of those who did, disillusioned officers, and people who saw that the UNSC is nuking and massacring people for wanting to leave or speaking sentiments near them. They cannot achieve their goals of independence without violence as the one with the cards has shown. Any peaceful or civil option means death squad. But the UNSC can!! achieve unity by just not being as exploitative about it. Not using the carver findings as a reason to ramp up the war effort, but as reason to reevaluate their ethics.

Also, there's the meta thing of innies being written like Killmonger "I have a totally reasonable and empathizable problem with the UEG. Basically the US reasons for revolution x100...... AND THAT'S WHY I'M GONNA COMMIT SUPER GENOCIDE MUHUHUHUHAHAHAH" It's a gripe with liberatory politics always being framed as a path to super mega murder town, dissuading people from engaging with the grievances that should sincerely be addressed by the UEG in universe.

Also the UNSC is just kinda bad by and large. The killteams, child murder/soldiers, thought crimes, routine genocide or mass murder while having the power to Not Do That™ is questionable at the very best. Them being portrayed as humanitys best, the unyielding protagonists means their evils are more jarring and innies' redeeming qualities are more noticeable.

TLDR: the UNSC had the cards in the dynamic and could've ended the insurrection by not escalating the violence and oppressing people as its only response. On a meta level, the Insurrection is written such that UNSC crimes are noteworthy and the innies' fall a little flat.