Part of the weight in Cohen's "animus-identification complex" comes from identifying with the demon-lover . . . while also feeling the ethical dilemma (for both himself and the other) in this identification. I don't think he is identified with the Demon (in my terminology) so much. But the animus is often confused with the Demon/demon in the experience/fantasy of many women. Demon/Self confusion is a major theme of all inner work. It makes things very sticky for every individuant. These are the two pillars of power in the psyche.
But with Cohen, I think of him as bearing a piece of archetypal suffering because of his identification with the animus . . . which is often demonized and mistreated by women. I'd think of it more like identifying with the beast (from Beauty and the Beast). It means people are bound to treat you like a beast much of the time. But do you want to be treated that way? Of course not. Beast is sensitive and sophisticated in many versions of the tale. The true heroine is the one who can see through the "enchantment" of the dark animus/Beast. She differentiates him and thereby "redeems" him.
The animus identified man gets himself caught up in the inner debate and conflict of the would-be heroine. If the woman he is involved with accepts the heroic role and "redeems" the Beastly part of the animus, then he (the animus-identified man) is also redeemed (just as he is allowed to redeem or inspire the woman). But if the woman does not make the heroic differentiation that redeems the animus, the animus-identified man is treated as an archetypal scapegoat by the woman he "courted" or tried to "carry animus" for.
For Cohen, the animus-identification (I believe) is part compulsion. It's his wound. But I think it shouldn't be completely pathologized. It's a romantic wound, a gambler's wound . . . not entirely unconscious. He chooses it. If it works out the way he hopes, everyone is better off for it. He is "redeemed" from his darkness and the woman finds her inner heroine. But when it doesn't work out this way, he suffers archetypal wrath from the woman . . . and that is the Blues, the grief in all of his songs.
Some of this animus/anima type exchange is inevitable in every romantic relationship. We can say it should merely be hacked off. It drives our romance. But it is dangerous. Real romance requires heroism and sacrifice. It requires transformation. In the song, fire transforms wood into smoke/ash (which is, of course, a symbol of spirit . . . that which rises up). Wood is raw, undifferentiated, "undeveloped", "feminine" material (by classic symbolism, at least . . . oh and see Sealchan's dreams of anima-wood, too). Smoke/spirit is blackened (Nigredo initiated) hero-stuff. The hero is an archetype of spirit (where "spirit" = a devotional and facilitating attitude toward the Self).
The carrying of these archetypal roles is also part of the therapeutic relationship . . . where we call it transference/countertransference. In general, I stand against the more psychoanalytic view that transference is a "problem" or something to be "handled". The soul is volatile. Relationship is dangerous. Intimacy is transformative. Psychoanalysis and developmentalist Jungianism place too much emphasis on depotentiating and wriggling out from under transferences . . . and tend to call intuition about the other/patient and affective reactions to that person, "countertransference" . . . instead of simply "relating intimately". You would think by these schools of thought that they had invented intimate relationship!
In my opinion, these particular analytic schools suffer from a fear of falling into "participation mystique" with the projection of the patient (where the analyst might lose his/her sense of power/status/knowing and become "like the patient" who, I worry, is unconsciously despised or looked down upon by some part of the analyst in psychoanalytically-influenced styles of analysis*) . . . and this unmanaged fear causes these analysts to be "besieged" by countertransference affects. My feeling is that we, as personalities, are not as fixed as entities as the psychoanalytic fantasy would have it. We are dynamic and flexible . . . even to the point of "bending over too much". We are like trees that take their branching shape from the complex conditions of the environment. We are not meant to have an ideal shape. Life and relationship bend and twist us . . . and sometimes we bend back while other times we stay bent. But we keep growing . . . and that shape, however twisted, is who and what we are.
Just a digressive little rant partly based on what I've been reading lately
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* That's a big side topic I won't get into right now, but I think this stems from a problem psychoanalysts and developmentalist Jungians have with trying to play Good Parent (or specifically Good Mother/Good Breast) too much for their patients. The idea of this school of analysis is that the patient is "contained" more or less unconditionally as an infant should be contained by the mother . . . in an ideal attachment relationship. Sounds nice, but is it really possible to become an archetype of such perfection and power (the Good Mother)? I don't think so. So what I feel happens is that the attempt to play Good Mother ends up casting a shadow (perhaps the Terrible Mother or maybe the Petulant Child) that the analyst tries to tie up in a sack. But inevitably, it pokes out and interjects "affects" once in a while. The psychoanalysts call these "countertransferences", and although they have started paying closer attention to them (as valuable indicators in the analysis), they still typically see these as contaminants from the patient's unconscious. I believe that these countertransferences are more frequently shadow belches from the bagged up Terrible Mother and Petulant Son that the psychoanalytic model places under great pressure/repression.
This isn't to say that the insights they give are "wrong". They might actually be wise and helpful. But they are still contents under pressure, and I feel a better way of modeling analysis would integrate these shadow polarities into the analyst consciously. The idea that the analyst should be the Good Parent the patient never had is, in my opinion, an inflation. And by forcing the patient to regress to infantilism so the analyst can play Good Mother is a power play that can quash the heroic instinct. There is no more powerful archetype than the Parent of the Infant. Even God in heaven is less mighty. But from what I have seen, the psychoanalytic schools have a complex or repression around this particular inflation. I think that asking an analyst to be a Good Mother is like asking a priest to be the representation of Christ on earth. It ends up creating a dangerous shadow. It's too far beyond human capability.