If Mundus is falling apart because the towers are becoming inactive, why not build new ones? White-Gold Tower was build by Elves, after all.

Lost art, and somewhat pointless these days. The original function of all of the towers has already been dealt with, as Adamantine and Crystal couldn't handle the strain of Red Mountain, Walk-Brass, Falinesti(?) and finally White-Gold going under. Their purpose is now a moot one, with the statue at the Temple of the One (Or just the event itself) have shut Daedric invasion from Tamriel for good.

Then what is all this talk about the Thalmor trying to deactivate all the towers to unmake Mundus?

As far as I am aware, the Adamantine Tower is still active. There may be a tower in Black Marsh that is active as well.

I honestly don't know where its coming from, unless there was a line from the Ask Me Anything that took place recently that I missed. The Thalmor's first and foremost goal is the eradication of Talos, and I'm not entirely sure what the towers have to do with him at this point and time. We already have seen what happens when most of the towers go down, and unless Adamantine has a special function, I can't see the Thalmor doing anything with it. If they really wanted to get to it, they would've invaded the Illiac Bay region, as opposed to slogging through southern Hammerfell and turning their eyes toward Cyrodiil.

I think the idea that the Thalmor want to deactivate the Towers comes from a little speculation backed by their stated goal (as per MK) and the original purpose behind the Towers, regardless of their current operation. The speculation bit comes from the fact that they were intent on invading and capturing Hammerfell, and only turned their full attention on Cyrodiil when they began to think that they could take it all in one go. The question becomes, then, what benefit would the Thalmor have in taking Hammerfell? I believe, and I think others do too, that the idea was to gain access to the Iliac Bay--and Balfiera Island. Sure, that's a complete guess, and other Hammerfell lore-masters could tell me what other possible reasons the Thalmor might want the place, but I don't know them myself, so I figure Adamantine is as good a reason as any.

Also, as far as I know, the purpose of the Towers is to keep Mundus from dissolving back into Oblivion, not necessarily to keep Oblivion out of Mundus--in fact, White-Gold Tower was originally used to attract Daedric influence of some sort for the benefit of the Ayleids, IIRC (I'm not exactly sure how else to describe it when White-Gold was acting as a creatia magnet). Akatosh flipped it so that White-Gold and the Dragonfires would keep the Daedra out, and that task might well be held now by Martin's Aka-statue, but that was not the original purpose behind the Towers as far as I can tell. We can't assume, therefore, that the purpose of the Towers is moot based solely on Martin's sacrifice. All that said, consensus agrees with you both that the Towers that are left are not having an easy time picking up the slack of the ones that have been "deactivated." But consensus also seems to think--or at least suggest--that Talos himself is picking up a lot of that slack, and so the Towers are just extra tethers that are supporting his efforts (or vice versa).

Now, possibly the Thalmor want to use the remaining Towers to get around Talos's protections. Possibly they simply want to snap more tethers as the "next step" in the plan. Or possibly the Thalmor think that manipulating Adamantine (the place where Creation effectively began) will allow them to reverse Creation altogether--it might not be about the Towers, so much as it might be about that Tower.