Welcome to Historum, Veronica.
I assume you mean the political leaders and not the paramilitary ones.
What would they fear from their own sides? -
In the event of any compromise (or 'surrender' - a very emotive word in the region) this could result in the formation of hard-line splinter groups from the existing paramilitaries to carry on the violence, even against their own side, who would be seen as traitors.
Both sides had plenty of 'volunteers' unfussed about using guns and explosives, it was a plausible fear.