What reasons did those in power during the reign of terror give for their harsh actions?

Answer 1

The primary belief of the leaders of France during the Reign of Terror, like Robespierre, was that the Revolution was constantly under threat of being overturned or reversed by subversives, émigrés, nobility, and numerous other people. In order to maintain the Revolution and prevent France from returning to the hated Ancien Régime, the government had to eliminate the insurrectionists. This led to the mass executions that defined the Reign of Terror.

Of course, outside of the four walls of the Jacobin-led French government, pretty much everyone agreed that the fears of betrayal and revolution-reversal among the Jacobins had risen to the level of paranoia and were no longer a legitimate safety concern.