Self-insertion
Empathizing
In essence, self-insertion focuses on placing yourself into the story, while empathy involves understanding the character's experience from within their own frame of reference, without necessarily making their burdens your own. Empathy allows for connection and understanding while maintaining a degree of separation, fostering a sense of shared experience rather than complete integration within the narrative.
Your conflation of the two, really falls short given that this is an incest game.
Stating that people who enjoy NTR content are 'cucks' is concerning because the logic of your argument implies that you enjoy incest content because you want to fuck your mom.
I'm going to assume that isn't true. And in fact you enjoy incest games not because you find your own mother sexually attractive. But because you enjoy taboo breaking.
All this is to say.
Maybe don't kink shame people.
People self insert to some degree through empathy, no you do not need to place yourself in the story, much media designed as a self insertion fantasy has characters with well defined personalities, of course you also have blank slates like Link or Joker.
Your right, liking NTR doesn't make you a cuck, but its technically the cuck fetish so its the only word I could use to describe it, same way this you say the incest fetish and yes most probably don't like the idea of their actual loved one's being fucked by others like genuine cucks.
But don't play the anti-NTR thing, ntr is infamous as a troll tactic.
As for why people dislike it. Imagine taking a hero and having them badly beat, not in a, they lost a tough fight, but in an emasculating, mocking way, they take Goku and they officially have Superman ram the American flag up his ass and its canon to the manga and then he bangs chi chi,
Goku is a character a lot of people live vicarously through, so its like an insult to them.
People just don't like to see characters they like be degraded and being cucked is degrading.