First of all, not a couple of millennia, way more. Second, from what he's seen, Yukina doesn't carry herself with any sort of confidence, which is funny as while the Yamato Nadeshiko archetype is supposed to be supportive of their spouse/partner, they also have their own opinions and will not hesitate to make their stance clear. Silk hiding Steel, if you will. Yukina, on the other hand, lacks the Steel from what Michael's seen. No self-confidence = no confidence in fighting ability = no fun to fight. There is a distinct difference between humility and a lack of self-confidence.
As for the knocking him down a few pegs, that idea was first made when Neo refused to apologize, not because he refused to apologize, but because he basically looked at someone who, from Michael perspective, looked way stronger (pissed-off pyromancer swordsman vs unarmed stoned Alchemist at close range, I don't need to tell you how that would go.) and already looked pretty murderous and basically told him to go fuck himself. That level of stupid is not one that Michael will suffer for any longer than he has to. Also note that Michael tried to separate Neo from Lorenzo, granted he wasn't particularly gentle about it. But the fact remains that he doesn't like Lorenzo interfering with the fight. Again, he was about to call Lorenzo out on it, but Yukina tried to shoot him.
And yes, Neo was offered a duel. But the point is not that he happened to be high when the duel was offered, but that he would get high in the first place, when anyone could pop in on the mansion. And Michael wasn't ticked about Neo refusing to fight due to being inebriated, it was because Neo gave the impression that his work on that so-called pancea would be severely set back by a quick spar. (Look at it from his perspective. A few minutes to fight, Neo heals up with a healing potion, which Michael expects that he'll have, due to his knowledge that Neo is an Alchemist, and then Neo can get right back at that cure-all.) The way he put it sounded like he was making excuses for himself, which is annoying.
That aside, Michael was also annoyed that Neo was inebriated in the first place, given that people can just drop into the Manor at anytime. Someone far less nice could potentially end up also in the manor, and if Neo is high at this time, it won't end well at all for him. So yeah, self-preservation instincts are hitting rock-bottom here from what Michael can see.
And Michael also offered to level the playing field. Then Lorenzo arrived and scuppered all of those plans, so Michael decided to make do with what he could get and try to get Neo to sober up, which he did, before actually starting the fight (Throwing him out the door was to separate him from Lorenzo).
That aside, I see your points on the actions against Yukina and have modified my post to have him trying to disarm Yukina and take her down. Though, given that Michael is moving at High Supernatural, he's attacking even faster, and Yukina's agility is human, I doubt she's going to be able to do much about it, especially considering what Kat said earlier.