I believe that it was during the 1980s when I became more than passing aware of the Yin Yang symbol --which, to my understanding, originated from the Tao (pronounced "dow", as "down" without the "n") --aka "Taoism".   The Yin Yang symbol represents the balance of opposites --in principle; in general; in the universe.   (I won't now discuss any details of its symbolism. You can easily get that info elsewhere.)   My life's experiences and at least a few things that I read --including various writings of C.S. Lewis-- gradually convinced me that a healthy balance of opposite inclinations is necessary for psychological / spiritual / emotional maturity & health.   I could expound on this topic for a while and I might add this at some other time but, for now, this is all I'll say about it.

      As for the phoenix ingredient, I worked as staff at the University of Chicago for 17 years, where the phoenix is the the central ingredient of the logo.   Being around this symbol for that many years, I sometimes thought of the thematic connection between the phoenix and that passage (at least one) in the New Testament (I don't presently remember the chapter & verse) that speaks of the purification of gold by repeatedly putting it through fire, as a metaphor for spiritual purification by enduring trials and tribulations.   A similar connection occurred to me, regarding a popular phrase, something like "Whatever [sickness or injury or hardship] doesn't kill me makes me stronger." (granted, an oversimplification but there is much truth to it for many difficulties that many people experience).
      The appeal of the phoenix specifically, to represent this principle, is (A) that the phoenix is an ancient and exotic symbol and (B) that the phoenix proactively chooses to put itself through what feels as though it must be the ultimate hardship --that is, to deliberately burn oneself to death-- in order to regenerate itself through a variation of rebirth, rather than simply waiting around for whatever hardship might or might not happen to come.

      I do not claim to be a Taoist, partly because I haven't bothered studying enough, about Taoism's particulars, to be able to claim that as a label for myself.   I also cannot rightly claim to have the toughness or the spiritual maturity to choose, altogether deliberately, to put myself thru intense hardships simply for the sake of increasing the purification of my spirit or soul or psyche; etc --it seems to me that life's happenstances have provided enough hardships for me, without my wanting or needing to deliberately seek out more.   (This principle appeals to me, which is one reason why I like the movie "Fight Club" very much, but, again, I ain't that tough.)   But I do claim that the Yin Yang symbol and the principle of the symbolism of the phoenix impress me as being important enough to justify one's placing them near the center of the symbolism of one's personal philosophy about how a human being should try to live his or her life on this planet.

      As for the graphic details of the symbol itself, this is a work in progress. I created something almost exactly similar during the late 1990s while at the University of Chicago and I published it on a web-page hosted by one of the systems owned and managed by the Biological Sciences Division, in which I worked. The primary difference is that the former version --of which I lost all copies after I left U of C and they took the web-page(s) down-- had only one head and I had added some flames to the bottom of the symbol, which I might eventually add to this one. I simply haven't had the time to do so yet, and I want to polish the existing graphics before adding that detail. I also have a few other Yin-Yan-animal ideas in my head but, as with the flames, they must wait until I have the time to create & develop them. (The two heads of my symbol have nothing to do with Freemasonry.)