Many apologies for the massive tl;dr ahead. I've been working on this post intermittently for a few days between a conference and rereading Facets' hilarious AoEx translation blog for the five-billionth time.
I think Toudou's fascination with Yukio was due to the apparent similar situation they were in. However, it turns out they are actually not similar at all. Although he didn't say it very clearly, it looks like one of Toudou's motive was that he realizes he will never surpass his father and brother(s) no matter how hard he works as an exorcist. And he did achieve higher accomplishment when he became a demon, so his choice is actually kind of reasonable. Yukio is different. Although he is also following Shiro's career path, as a 15 years old boy he just started the career and doesn't have any reason to believe his accomplishment is limited. Then Toudou tried several ways to attack Yukio's mind and finally one of them seemed has effect : Yukio does envy Rin. However, Yukio does not envy Rin's power or strength (at least at IK arc). It was Rin's personality and the possibility that Shiro loved Rin more. Clearly Yukio can't gain anything if he joins Toudou so he won't. At the end Toudou realized that their problems are different. Then he laughed at Yukio's "both love and hate my brother" and commented it as childish. Toudou even tried to kill Yukio until the blue eye incident happened.
Therefore, in my opinion their interaction is already over at IK arc and Toudou doesn't have any more things to say. Toudou was correct that there is a dark/demon side inside Yukio's mind, but I think it is quite common among human and is not enough for a person to actually go evil. Then Toudou reported Yukio's case to Lucifer, and we have seen Lucifer did find the right way to approach Yukio
Gonna disagree. Toudou started the fight in Kyoto with Yukio simply to understand Karura's limits. He was playing around and not fighting seriously. That allowed Yukio to get the drop on Toudou with the naiad trap. Toudou was impressed by that but figured Yukio was just a boring ol' human and not worth the effort to manipulate, so he attempted to kill him. Thus when Yukio manifested a demonic ability, Toudou was pleasantly surprised and said he underestimated Yukio -- AKA Yukio was now worth the effort to turn.
After he felt he had a grasp on Karura's abilities after fighting Juuzou et al., Toudou got serious. After restraining the others, he proceeded to tear apart Yukio's self-loathing complex. He pointed out that way of thinking was self-denial and had limits. He was right. Yukio uses self-loathing as a coping strategy to keep himself centered, a daily reminder that his envy and resentment were bad especially in relation to Rin and he shouldn't indulge it. That meant he never learned to deal with the root of his resentment. Toudou then pushed on how Yukio was already well on his way to becoming a demon, linking in his envy of Rin who's also a demon (later was paraphrased by the portrait demon) and emphasizing how being a demon is totes awesome. Note that in all the time they were fighting, this is when when Yukio started to lose his temper. Facets did
a really great analysis of what Yukio says here. Toudou's parting words that Yukio has a "nice look, the face of a demon, that's your true nature" hit Yukio hard because Toudou wasn't only saying that Yukio has a dark side, but implying that Yukio will inevitably become a demon because that's what Yukio is.
Fast-forward to now. Yukio's inability to confide in anyone has led to the suicide training, the failed attempt to get access to Hachiro's powers, and generally poor mental health. He's been acting progressively more demonic and hasn't been catching himself. He's gone from "if I were in your shoes, I would've gone crazy" to "just give me your flames" to quoting what Rin said in the Whale arc about them really being siblings who will never get along. Yukio's given up on his self-loathing and has accepted that he and Rin aren't alike. That's two coping strategies gone. He still is on the TC Order side out of sheer stubbornness (ah, Mr. I-Don't-Need-It), but he's slipping. His laughing in Rin's face feels like a portent of what he will act like as an honest-to-god villain. It makes me worry that Yukio could actually fall into exactly what Toudou said in their first meeting, that accepting his weakness and hatred would feel wonderful. So far the rest of Toudou's prediction has been right.
Toudou kicked the case upstairs to Lucy not because he realized they were different, but because he badly wants Yukio on their side and Yukio is too stubborn to listen to Toudou. Plus, Toudou got the information and did the groundwork that allowed Lucy to tempt Yukio in the way he did. If Toudou did realize they were different, I think his interest in Yukio would be long gone. But instead in his most recent appearance, he said "I like that kid", which was a biiiit more suggestive in the original Japanese. I believe Toudou's interest in Yukio is borne out of his own self-absorption, and that by pushing Yukio to the Illuminati, he is "helping" himself. Toudou doesn't really see Yukio Okumura, but a version of himself. That's Toudou's biggest weakness -- his arrogance.
Yukio has tried to refute Toudou before by insisting he's different. It doesn't work because, well, they are similar. They are both strategic, manipulative, and resentful. They do have critical differences. In particular, Toudou's given up and can't change. Yukio never gives up. His stubbornness is his greatest strength and weakness.
The story between those two isn't finished. Toudou is Yukio's nemesis, just as Lucifer is Mephisto's enemy and Satan is Rin's enemy. Rin intends to physically defeat Satan. Lucifer and Mephisto are waging war on each other through their pawns. Toudou and Yukio's conflict is about
"making your enemy see they were wrong to oppose you in the first place". Yukio will win eventually, not by physical strength but by proving he is right.
