Maybe they hate President Deling since we all know he is a dictator before he die.

The soldiers value their life more than loyalty and switched sides of course. They dun want to end up dead as they saw a live example Edea make out of Deling.

But this is just my opinion though.

BTW, do anyone notice this? When Squall drove the car and charge towards the spot where Edea is trapped, he just jumped in where Edea is while there is a gate and the very gate that trapped Edea BLOCKING the way.