Ti and Te.
Fi and Fe.
Si and Se.
Ni and Ne.
These function pairs just don't get along when acting as dominants in two different people respectively.
For example, Ti and Te doms are constantly at war with each other. The relationship could be characterized as nerds vs. bullies. Fe doesn't bother Ti nearly as much as Te. Fe may only seem annoying to them in comparison. Fi and Fe I've heard tend to quarrel over matters, but I'm not sure why.
Si and Se - I've seen Se react strongly against Si, but I don't know why. And I don't know what kind of sparks fly between Ni vs. Ne.
Looking for answers here...