You probably misinterpret the whole thing.

There's plenty of reasons why Taim would feel that way, even if he is just Mazrim Taim.

Think of Logain's problems to adjust to Rand's authority over him. Logain ressents it a lot, and make a show of that. With Taim, it's just worse.

Think of Mazrim Taim as another Barid Bel Medar. The man is full of himself, and from the get go considers himself Rand's superior, yet Rand is extremely arrogant towards him. He expects to be at Rand's side and his equal, but Rand orders him flatly to go teach beginners at a secluded Farm. If Taim was a DF then (which he most likely was), then this ruined the orders he was given. This was also humiliating, and this probably grated Taim when his Forsaken master ordered him to stay at the Farm, and use this position to build an army, to make the efforts to increase the numbers as much as possible. To actually work, not just parade at Rand's side waiting to betray him.

As for the pins, put yourself in Taim's shoes. Rand let Taim run the show at the BT, but suddenly without warning he comes, changes what's established and acts again like he's the boss. Worst, he make a public stunt of showing Taim isn't more than another Asha'man, the first among equals at best, and definitely below Rand himself, who isn't wearing the insignas. Taim once thought he was Rand's equal while feeling he was his superior, then was put in charge of the Farm, and now he's being shown publicly as only the equal of the others and the boss thanks only to Rand. Some men would feel proud, like many Asha'man do. Taim isn't that sort of man, no more than Barid Bel Medar was. It's said LTT bestowed honours on generals like Bel Medar too, and he ressented it and hate it, just like Taim does.

There's also the fact Taim was most probably given instructions on how to best run the Black Tower, and foster loyalty among the men to himself instead of Rand. With his ranks and rules, Rand was interferring in this work. Taim wanted to be the one from whom rewards and ranks came, and he didn't want the men to be reminded his authority came from Rand.

The result was that Taim circumvented Rand's system at the first occasion and created his own ranks and rewards, that would only came from him. That's when he proclaimed himself the M'hael too. He started to play on the fact Rand didn't have a title at the BT, didn't know the ranks and wasn't the one awarding them.

There's nothing in Taim's profile and scenes that can't be explained in another way, often better, than having him be a Forsaken in disguise. Even the "so called Aiel" may be a misconception. Taim may simply have not believed Rand's Aiel were truly the mighty "Aiel savages". It stunned many people that Rand got the Aiel behind him. It took a while for people to believe that.

It's even fairly obvious in WH, after he was pissed about the plot to kill Rand in Cairhien that failed, and he wanted to keep Taim in the dark about the mission he was now giving a bunch of Asha'man, that Demandred is involved one way or another with the Black Tower (and he even used Taim's title to speak of the man - as if he didn't want to undermine Taim's status with his faction), but he wasn't yet in the place himself, his main contact was with Taim, and with a few DF Asha'man, it appears. The place, how it's organized and all, screams "Demandred", and so do the "special classes" and the whole idea to undermine Rand's army by under-training it while the men loyal to Taim got the really nasty stuff (it also baited the men to join Taim for more power), and even Taim's attitude seems to indicate he's been told tons of contemptuous stuff about Rand and LTT even before he's met him, the sort of things Demandred would tell Taim. Sammael too, but we know Sammael was not involved.

I'm pretty sure it will turn out Mesaana had the BA free Taim, and Demandred went to him and convinced him he was Rand's superior and while he couldn't be the Dragon Reborn, he could be much more by serving him and the Shadow, and Taim gave in to his greed for power. The attempt to place Taim in Rand's inner circle, where he could spy on him and betray him eventually, and where he could influence the few men he gathered to him failed (it appears the Shadow failed to understand initially that Rand intended to test all men who came to him, not just welcome "wilders" who would have been few and far between. This news came from Taim, after he met Rand) . But Rand offered the Shadow a golden opportunity to mount an army of channellers hidden in plain sight instead, one that could eventually be joined to the Black Ajah. I'm convinced it's Demandred who seized that opportunity, and it would notably explain why he's so secretive about his plans with the other Forsaken but Mesaana and Semirhage, and how he insisted on keeping Sammael in particular away, later Aran'gar. No Forsaken but Moridin as top boss would be too pleased to learn Demandred was creating himself an army of channellers - even Mesaana would be lukewarm at best (and made no real effort to keep as many BA in the Tower, and alive, as possible). She might well think this way if she knows in the end they would all go under Demandred's command. By Graendal's comments in TGS, it seems even she has not thought Demandred would be clever yet arrogant enough to go build himself an army of channellers under Rand's nose, and Demandred was clever enough not to show the others how much power he had gained. Demandred even hinted at that, speaking of Sammael and how Sammael always had to show his power, and how he couldn't, like him, remain hidden in the shadows.

My guess is that it's been Demandred's plan since LOC to eventually step in as supreme commander of Taim's faction plus the Black Ajah (what he intends to do with this army in the LB may be more impressive/surprising than the fact he's gained this army). Meanwhile, he's got Taim to built the BT from the ground up, and himself had all the free time he needed to have many other plots going, and to observe things from afar. A plan to eventually take his place at the BT would also explain why he was surveying things in Caemlyn. Demandred is shrewd, and not the sort of man to set up somewhere without studying all the variables around first.

The whole affair of the "alliance between rebel AS and Taim" also suggests this. This didn't come from Aran'gar for sure, it's part of what ultimately forced her to abandon her mission... But... it did come from the Shadow (the Sitter who brought it up was BA). It probably was a way to steal the initiative from Rand, as this alliance would come eventually after saidin was cleansed, and Demandred had seen first hand Rand begin to use mixed gender circles again, a new development originating from the cleansing, not something that was in the cards before. Better then to have this alliance tied to Taim instead of Rand. Once this alliance was in place, this also let Taim begin to welcome BA openly for "advanced training" and mixed gender practice, as the Shadow now knew they'd need that against Rand's forces now. Once, Taim could have done this without raising suspicion - as long as the BA who came remained hidden - but after Logain started bonding sisters, the channelling of saidar would have been detected. Once the "alliance" was in place, though, it would become normal for AS to practice with Asha'man. It's very likely Taim would have refused the rebels to bond Asha'man, but he would have agreed that sisters come to train with men, and that a few Asha'man joined the rebels to allow big circles. As he's done with the men, he would let the rebels struggle with the Asha'man to find out how this worked, while only BA visiting the BT would get the "special class" stuff...