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For all his fondness of the "truth" there are little things that Tsukumoya's mind will instinctively dart away from if he starts considering them too closely. He never really considers them falsehoods but they do all seem to share a common theme of "uncomfortable thoughts involving Orihara Izaya".
The concept of "attachment" is one of those things.
Their relationship is a loosely defined thing at best. Founded in careful mind games and entangling words. Certainly there is a degree of comfort there, an easy sort of familiarity. But "attachment" is something that doesn't quite seem to fit. Attachment seems to imply devotion. A faithfulness that just isn't quite there.
As far as Izaya is concerned, sex is a means to an end. It's never been something he particularly cares about or puts a great deal of stock in. Sex is another tool to be wielded to carefully push people into doing what he wants them to. For Izaya his "love" for humanity is not connected to sex. He's gone off on tangents about it before that Tsukumoya has listened to in a half-interested sort of way.
None of this really matters to him, but he understands. Mostly.
Human emotions are abstract concepts that he has mostly pieced together through observation. He doesn't really feel such things himself and for the most part he finds the idea of any kind of emotion interesting but irrelevant to him.
And sex? Well, sex is a tangled mess of biological impulses that he is incapable of feeling. If Izaya is his only partner it's simply because he lacks interest otherwise.
Lack of interest and the fact that explaining his... unique circumstances isn't quite something he wants to deal with.
So the simple fact of the matter is that there is no reason for him to feel anything in relation to Orihara Izaya. No attachment and certainly not anything akin to possessiveness. He even made a point of mentioning it to Shizuo once, as poorly as that might have ended for him. What he had said then was still the truth. Jealousy is a highly human concept. One that makes no sense to him.
The fact that he suddenly finds himself feeling twitchy and irritable while he watches Izaya deal with Shiki in his... usual manner makes no sense.
Worst of all, it's the sort of senselessness that his mind doesn't even want to attempt to understand. Skittering clear every time he starts to consider it too closely. All in all it's strange and annoying.
A little bit like Izaya, really.