It's obvious Fel had discovered something very important. I to belive it's a thing bound to the cleansing of Saidin(because Rand and Fel had spoken about breaking the seals...and this is certanly a subject connected with Saidin). I belive the most important thing to understand how Saidin was tainted.

LTT was unable to rebuild the prison as it was(thanks to the Posae woman) and created a shield of saidin held by the 7 focal points, the seals. Now the DO is breaking the seals because he can touch them and eventually he will break free, but he cannot break free from his old prison cause it was perfect and needed someone to drill a hole,after it has been done he could enlarge the hole touching the world. We know,from "The strike at Shayol Ghul",that the DO had almost freed himself from his prison and the chosen had been summoned to SG. But an istant before he could leave his prison TA-DAAN Lews and the hundred companions stroke!They posed the seals and imprisoned him again. But doing so they cut off the part of the DO already out.This part ends connected to Saidin (used to place the seals) and was held there by the seals themselves.The result was the end of the War of the Shadow and the beginning of the Breaking. Then the taint is a consequence of the DO's imprisonment. Destroing the seals will clean saidin but also free the DO. I believe that the true essence of the DO is the True Power,in the seventh book moggy says the TP is drawn directly from harthfang and it is more addictive and dangerous to use than the one power this would explain the horrible death of male channelers(channeling they meet the corrosive true power that,according to moggy,causes a really terrible death) and the reason way even harthstone can be destroyed(Because the TP is the essence of the DO and this is a power strong enaugh to break even Cuendillar).The TP has worked as corrosive for three thousand years and now it's almost able to destroy the seals. Probably Fel has discovered this and so he has been executed. Now we know why he has been killed(I hope...) another question has to be answered: who could know Fel's discovery? (Due to their personalities I belive Ishamael orAginor/Osan'gar)

P:S

Way so many people do not understand the Gars are Balthamel(the letcher-Aran'gar) and Aginor(the mad scentist-osan'gar),it's confirmed by the descriptions in the guide and by their beavihor (For example ,Grendal has said that aginor created the Trollocs and Osan'gar has thought he has created the Trollocs...for Balthamel halima's beavior is (for me) a prove he has benn resurrected.