Aviendha's toh
As for that relationship between Rand and Elayne and Aviendha, we have the heretofore inexplicable mystery of the toh Aviendha believes she has to Elayne. She has toh to Elayne for her relationship with Rand and she has toh to Rand for saving her from Lanfear. These are fairly understandable, but what confuses is her assertion that she could obviate one toh by suicide and the other by killing Rand, but the existence of each toh prevents her from using that solution to the other. In other words, she cannot meet her toh by killing Rand, because she has toh to him, and she cannot meet her toh by killing herself because there is still a toh for her to meet. Since even the weirdest twist of ji’e’toh cannot possibly explain how she could meet a toh to Rand by killing HIM, plainly her suicide is the acceptable solution for her toh to him. The wherefores of this are easy to extrapolate – by taking her life, she removes the thing that creates her obligation to Rand. Since she forfeits the thing she owes him for, she is no longer a beneficiary of his action, and therefore is no longer under obligation to him. Simple enough in a perverse sort of way. The reason she does not undertake this solution is that she perceives a much greater obligation to Elayne, which would be a disgrace for her to die without meeting it. According to Aviendha, and by process of elimination, one way to meet her obligation to Elayne is to kill Rand. Even taking into account the more casual Aiel attitude toward death and violence it is hard to see how she can meet a toh for partaking of what belongs to another by depriving the other of it altogether. The logic goes something like: Elayne wants Rand, Aviendha interfered, so she’s going to make it up to Elayne by getting rid of Rand. And that seems absurd no matter how you cut it.

The key to this one, I believe, is partially that issue of reliability, and in part due to the economic arrangements of the Aiel. Aiel women are the ones who own fixed property, specifically land and buildings, which have great significance to people in a hostile environment, as “shade.” The wife owns an Aiel married couple’s house and owns the land on which whatever crops they eat are grown. They also practice other trades, including trade itself, and other crafts like weaver or silversmith. With warfare being so endemic to their society, fighting and raiding would be the occupation of a majority of Aiel men, and that is not very lucrative. The plunder a man brings home would seem to be valued as decoration, rather than financial gain, which explains Rhuarc’s wife’s reaction to the gifts offered by her guests – she comes across as a bit unseemly with her rhapsodizing about gold and silver gifts and loot, but that is to our eyes, who are used to thinking of gold and silver in terms of wealth. She is discussing them for their beauty, and she means it(see above re: Aiel meaning exactly what they say). In modern culture talking about the beauty of a valuable possession or gift is a kind of deflection from appearing greedy by appreciating the financial gain too much. Among the Aiel, the beauty of the object is the central point, since gold and silver don’t buy much that Aiel value. In any event, with the major contribution of an Aiel husband to the household finances thus dismissed (their loot only brings in aesthetic décor & trophies, not monetary value), we see that marriage for an Aiel woman is a serious financial commitment, as the responsibility for supporting the household devolves largely upon her. This would also go a long way to explaining why Aiel women are the ones to propose – it is her responsibility to support the family, so she is the one to decide when the time is right to start it – and how a husband might have less input on the addition of a second wife to the household than might be expected. It is the women’s decision to go into what amounts to a household partnership, and they are the ones pooling resources to support the children, etc; all he brings to the table is defending the roof and sperm donation, and since the offspring are considered primarily hers, that contribution is socially minimized as well.

This is a problem for Aviendha, because Elayne has expressed an interest in marrying Rand. Not to him, of course, but then for the Aiel, the groom is the last one to find out. Aviendha’s blindness to such customs among the wetlanders is not helped by her wishful thinking trying to come up with reasons why her fore-warning of their eventual relationship cannot come to pass. With her mind fixed in this direction, she has to accept Elayne as committed to Rand, since Aiel always do what they say they will, and Elayne has expressed (or Egwene has on her behalf) a clear intention to marry him. And now, Aviendha has made Rand used goods. Even worse, he has made suggestions regarding marriage towards her, which might be construed as having undermined his affections for Elayne. Now that she has accepted her feelings for him, she is conflicted again between her honor, which dictates she follow through on her promise to maintain and uphold Elayne’s claim, and what she wants, which includes that relationship for herself. This might seem like petty emotional BS that can be gotten around from our point of view, but in the Aiel perspective of relationships, shaped by the violent necessities of life in the Waste, the feelings of a man can be important, despite what might seem to be their total marginalization in a marriage. With all economic and reproductive aspects of an Aiel nuclear family placed firmly into the distaff sphere of influence, it might seem like the men are purely ancillary figures in their families, but to the Aiel, fighting is all but a day-to-day necessity. The men are important as fighters, in a land where having something consists of the ability to defend it in battle as much as possession. What man will fight for a woman he does not love? Even if this is not Aviendha's direct reasoning vis a vis Rand & Elayne, that is probably the basis behind the Aiel view of relationships. That would be why she is so amenable to the idea of Elayne or Egwene killing Berelain to get her out of the way, or why Bain & Chiad, despite their refusal to intervene on Faile's behalf when Perrin spanks her, later plot violence against him for revenge, or why the Maidens go to such extremes with Isendre regarding her attempts to seduce Rand, despite his own inattention and lack of interest. Due to the life-or-death consequences of a husband's wandering eye, Aiel culture has developed an extremely negative view of attempts to subvert such bonds of affection (and might also explain the humor of the referenced joke about a man ending up married to the wrong woman - the absurdity of such a situation would be of a nonsensical scale). Thus Aviendha killing Rand as a solution makes sense – she sacrifices her own illicit desire and releases Elayne from the obligation Aviendha believes Elayne has incurred toward Rand. She also removes the object of contention between them. This is a reasonable solution among the Aiel, where life can be cheap, and honor and duty are much more serious considerations – however appalling the wetlanders who are the supposed beneficiaries of that solution would find it.