On inversion and transitivity

Peace and blessings to the Rabbi,

In a lesson on the subject of majority decision-making in halakhic law, the Rabbi's question was raised as to whether there is a "thing that has no opposite." I would like to offer another example to the one that was raised –

For any division into two equal parts, the inverse (at least according to the simple definition of – "give this part of this and that part of this") will give the identity function.
Of course, one can wonder whether such an example is valid for attributes and not just for objects (and then I just gave a private case of the example from the lecture), since it is difficult to accept a statement about a person who is "half-loving, half-hating." Such statements are usually accepted if they are said in the manner of Ecclesiastes – on the timeline or if they are dismissed as the imaginations of a poet, a kind of Rachel's words – "storm and blood, joy and weeping, / wound and affliction, rest and death." However, this situation is possible when talking about a public and trying to analyze its position. This leads me to another example, which is any preference relation over more than two options. The attempts I have made so far to define inversion preferences on the nth order have led me either to a contradiction or to the need to define inversion in a way that is very far from the intuitive way (and even then, I fear that inversion will not be possible).