The Cossacks were traditionally allies of the old regime and enjoyed a large degree of autonomy under the Czars, having Cossack villages with local autonomy in exchange for fielding cavalry. Thus they were generally loyal to the old regime, joined the white armies and resisted communist influence.

Like the kulaks, they were a group that had benefitted under the old regime and stood to lose a lot of their autonomy and economic freedom under the new regime, and thus resisted it. The communists responded with repression of cossack culture, autonomous villages and extremely harsh reprecussions to any resistance.

The cossacks were a social rather than an ethnic group through, as were the kulaks.

The communists did want to eliminate both the kulaks and the cossacks as social groups and include them both into their collective farm system.

However, the communists did reverse its policies in May 1936 and onwards - while the cossacks were not allowed their autonomy back, the communists attempted to revive their martial tradition and prowess as cavalrymen inside the red army by raising cossack formations and renaming units that had conscripts from areas with many cossacks into cossack units.

The Cossacks have always been outsiders. Since forever, the Tsars would bribe the Cossacks to guard the borders of the empire. Sometimes, the enemies would bribe the Cossacks more to stand down. Other times the Cossacks would rise in revolt, such as in Pugachev's Rebellion.

The Cossacks choose to fight the Soviets rather than bow to tyrants who wanted to control them and end their way of life.

First the Cossacks allied with the Whites, then later with Germany.

That's why.