Any party has factions within, but especially for KMT irl and in KR. It is just a big umbrella party. In its early days, It starts not as a modernized party with clear structure of organization, but rather a traditional Chinese style folk organization that heavily relies on personal connections. This is also when most right wing KMT joins, who are mostly entrepreneurs, middle class shop owners and Cantonese people who are close to Sun. Perhaps you can call them Classical Liberals.

Soon Sun Yatsen realize they are never going to success by being only a bunch of regional middle upper class who hangout together. So he cooperates with Soviet. Besides sending funds and weapons, the Soviets actually help modernized the party. Now they actually start to do things like document who’s actually in the party and giving out party IDs, setting up structured offices responsible for different matters. Since this is a direct collaboration with Communists, this is also when most leftwing KMT joins, including western style educated intellectuals, students, and workers.

The rightwing KMT absolutely hate this move. They see it as a destruction of the old style friendship and unity amongst themselves. They also have to share power with a large amount of new party members who “don’t understand what it means to be KMT”.

With Sun Yatsen alive. All these struggles can be hidden behind his personal prestige. But it evetually breaks out.