What does Asuka and Rei's contrast represent?

They are constructed as philosophical opposites — or, more precisely, as two different failure modes of selfhood.

Rei Ayanami has almost no ego. She exists in relation to Gendo and the mission, without strong personal desires, identity, or attachment to continued existence. She is self-effacing to the point of dissolution.

Asuka Soryu has an enormous, rigid, defended ego. She has constructed an iron identity — the best pilot, the most capable, the most impressive — that cannot admit vulnerability or failure. She is self-protective to the point of isolation.

Both are variations on the same problem: the failure to integrate the self with others. Rei has no self to share. Asuka has a self she cannot allow to be seen.

How does Shinji relate to both?

He exists between them, without either's extremes — and without their certainties. His passivity is not Rei's absence-of-self and his vulnerability is not Asuka's defended pride. He is genuinely unable to commit to existence, which is its own mode of failure.

The three pilots together map out different ways a person can fail to inhabit themselves fully — which is part of why the series resonates so specifically with a generation that felt similarly lost.

Why do fans divide so strongly between Rei and Asuka?

Because they represent genuinely different needs. Those drawn to Rei often respond to her stillness, mystery, and the sense of something beneath the surface. Those drawn to Asuka respond to her expressiveness, her fight, and the recognition of her wound. Which character you respond to often says something about your own tendencies.