This topic is based partly in personal experience, and is a short hypothesis on the underlying dynamic that occurred in that relationship. I don't mean to imply that the idea stated here is highly substantiated, but is merely food for thought and a post intended at igniting some Socionics-related discussion on the board. If I don't make quite as much sense as I should, feel free to ask me to clarify and to question me for more detail.
Supervision has often been considered to be a very painful relationship classically, even moreso than conflict because the supervisor can exert more pressure on one's weak functions than one can place on his. I, however, have come to understand supervision as a damaging premature entelechy, supposing that duality results in a full and wholistic display of oneself. The fundamental idea is that a supervisor causes one to exhibit behavior one would only see in someone who is very dualized, and This behavior does not result from an internal strength derived from a dual relationship, but a mask imposed by the supervisor externally. (This stems from the idea that one derives a well if lasting strength from a dual.) Once one is engaged in the mask imposed on himself by a supervisor, he finds that life often seems grand, as if he's in the summer of his life - - and This often happens very quickly. But because this behavior is really very superficial, it requires a massive amount of energy to maintain on the part of the supervisee, which in the end causes a crash and burn experience, because this behavior does not come from one's own nature, but is imposed. One acts constantly as if one should act rather than as he is. In a dual relationship, one preserves his fundamental identity and over time becomes seasoned by his dual to occasionally take trips into dual territory. When this however is occasioned by a supervisor, a person is shocked into a completely opposite character in contrast to his nature: for instance, an ILI becoming compulsively social after interacting with an EIE. Other people can see this behavior for what it is, as shallow and trivial, but it often feels like the font of life itself for the one engaged. This usually results in neurosis, as the energy to maintain this mask fails, and the supervisee returns to himself after breaking away from the supervisor or developing a tolerance to the supervisors method of imposition or primary function. When the supervisee finally comes away from the experience, which might be years later, he often feels cheated, deluded, and bitter. This thing that seemed so great and amazing so quickly ended in catastrophe for only one party. And it took so long to figure it out and put his life back on track. Now he's right back where he's started, none the richer for all the effort spent.
In the case of duality, one's dual is often a connoisseur of certain traits that he might like to see in his dual, but even if those are never displayed, he still finds his dual to be a worthwhile and valuable person. As such, duality promotes an experience in which one can grow without being forced to, or go simply remain as one is and still be considered. Supervision demands in the most tempting way possible the premature growth that one only finds in those who have been growing for a very long time.
This might bring up the objection that one's dual doesn't value at all the dominant function of his supervisor. I agree with this statement; there is really no contradiction here. In the above example, where the EIE demands Fe from the ILI, an ESFp would ask for Fi. Both of these are F, but simply from another perspective. The extroverted counterpart is wild, forward, objective, and quick, while the latter is a bit more nuanced and receptive. The difference in life can often be very subtle but very important.
I hope this helps and doesn't sound too much like an indirect biography of myself, or that I'm trying to warp a theory based on personal experience. I ask that those who read this consider the ideas in themselves. I most likely am not 100% right, but I do believe there's something there.