And you're still incorrect based on what we actually saw in the books. How is it possible that a woman couldn't teach a man how to channel Saidin when we know for absolutely certain that she can demonstrate the weaves to him and so he can copy them?
No. When a channeler of 1 sex is linked with the other, they draw power from the other but still channel the way they regularly do.
For example, when Grady (Perrins asha'man) links with with the Aiel Wise ones, he creates gateways as a male does. This also works for a female.
Infact, there is only one example in the entire series where we see a female channel saidin-style. This is when Semirhage has Rand collared, and due to the unnatural link created by the a'dam, she is in control of his channeling but not TRULY linked. When she tortures Min with OP, Semirhage says:
He righted himself by her command, the room growing more steady, the nausea retreating. And then he began to form weaves, complicated ones of Spirit and Fire.
"Yes," Semirhage said, almost to herself. "Now, if I can remember... The male way of doing this is so odd, sometimes."
Rand made the weaves, then pushed them toward Min. "No!" he screamed as he did so. "Not that!"
"Ah, so you see," Semirhage said. "You weren't so difficult to break after all."
In short, a female can teach a man ONLY if she knows how saidin is woven. Simply linking and weaving stuff is not sufficient (because its woven saidar-style, and won't work when the male tries it alone without the link).
Now this is certainly possible if that female has spent a LOT of time learning how saidin is woven, and she actually knows how saidin is woven directly. In this case, links obviously work as a teaching tool. This also would work in reverse however, (if a man has spent lots of time learning how saidar is weaved). But if not, linking won't help. Apparently Ithroen is not familiar with how saidar is woven, so we have no reason to believe Tavar would be familiar with Saidin either.
Where he lights his pipe at the very end.
This is after Perrin basically confirms Rand is no longer a ta'veren.
Rands ability is unknown, but most likely something to do with his exposure to the reality outside the pattern. Though thats speculation too. Ultimately we don't know, and never will.
You will never be able to prove that this was ta'veren, because according to Sanderson, RJ explicitly left notes saying that Rand lighting his pipe with his mind was something that was supposed to remain mysterious abillity that will never be explained.
