As Takumi pointed out he knew that Eizen was going to try to screw him over somehow, since that's all he does. So he made a dish that their was only one way of screwing it over then made that dish to counter that attempt. The thing is with Eizen is he is the only dis-likable and despicable member of that group (especially since Erina [the original antagonist] and Kuga joined the good guys.) So if your going to make the Elite Ten the bad guys you kind of have to focus on him.
Erina has never been the antagonist, she's been the rival of sorts, she's never done anything to antagonise them, her actions were down to her conflicted feeling, where Souma's techniques clashed with her teachings. even the Kuga battle, you couldn't consider him the Antagonist as it was Souma that sought him out and challenged him, Kuma was a competition, these two would not have been considered antagonists even if they had joined the Elite 10 (well we would likely see a personality shift from Erina as she'd likely be emotionally cut off under the control of her father.)
Even now the rest of the elite 10 seem to behave like competitors than actual antagonists, so he just sticks out like a sore thumb, this is the fault of the manga by design. Concentrating on Eizen would be fine if not for him already being shown to have been beaten at his own game, the Karage arc, the dorm closure arc, these are all defeats by him, and lets not forget Eizen is the weakest member of the Elite members, and even if he is the only one that behaves like a antagonist, he's still the weakest link (after the throw away members in the first round).
We've already been given details of his underhanded techniques, we had it pointed how he is known as the alchemist in both his previous defeats, so there was really nothing new to bring to the table, if anything this should have been a perfect opportunity to show him use his alchemist ability to defeat Takumi on talent alone instead of using underhanded techniques, we could see clearly his defeat to Souma affected him, so it would be fair to see him go beyond his usual tactics to secure a win, but instead the mangaka chose to have him stand still.
This was done to so show Takumi has overcome his previous lost where he was baited into making a error and walking into the trap the copy-cat had set for him...instead he took what he leart in that loss and baited Eizen into walking into the trap he had set. I guess the moral about this match is learning from your losses, Eizen didn't where Takumi did.