I'll answer this question rather brief cause I don't have much time.

The primary reason for these Soviet claims was to prevent the possibility of unrest. This was a typical tactic used by the Soviets, this even happened to Soviet ambassadors. (for a varity of reason just so they couldn't expose how bad things in the USSR really were compared to the west.) By deporting people away from their ethnic home they could assimilate that cultural group into the USSR with less tension from the people living there as those they saw as "resisters" were sent to Siberia. The fact that the Soviets accused the people of Chechnya was basically an excuse to deport them.

Source This isn't the original source of my information but it gives you an idea of what I'm talking about.