Because we're human and we're finite, so sometimes we're right, sometimes we're wrong, and sometimes we disagree on the definition of one or the other. I don't think it's indifference. Because we're finite and come from different environments and make independent choices, we come to different conclusions. And sometimes those conclusions are simply incompatible.
Is the real question how to prevent a church, family, etc. to split apart? If I had the answer, I'd tell the entire world. But the problem isn't a simple one, and people much smarter than you and I have struggled and failed to come up with a foolproof answer.
We can love and work towards unity, but sometimes unity isn't possible. No, I will not take my sons to that church if I know the priest is a pedophile, and if that creates a church split, so be it -- but I will not allow my sons to be emotionally scarred for the rest of their lives. No, I'm not going to advise my sister to stay with her husband if he abuses her every night -- no matter how much she says she loves him. I love her too much to say they should be together in the name of unity -- sorry. No, I don't think it's healthy for the nation to allow slavery and segregation in the name of "unity" -- I believe people should be free and should not be judged by the color of their skin, and if that every means I have to take my rifle and risk my life in a Civil War, then so be it. It's part of the human condition that we have to go on in spite of our disagreements and the anguish involved within them, and that we have to keep learning how to love in spite of the hate that surrounds us.
I don't know if that was the answer you were looking for, but it's the best one I can give you at the moment.