because Rand is the Car'a'carn, the whole Aiel nation are obligated by prophecy to follow him to Tarmon Gaidon and to be broken by him. Aviendha cannot kill Rand to fulfil her Toh to Elayne because doing so would mean that her entire race could not fulfil the obligation of prophesy or their vow to spit in the Dark One's eye.

By killing Rand over it, Aviendha would have doomed the entire world as well. That is why she had no way out of her Toh, even though it might have been the only way to fulfil it.