I felt @
Jeb_CC 's explanation is really impressive.
To me, identity is like an art, in many ways.
As a well-known concept, therianthropy is explained as an 'innate trait', a sort of 'born gift'. I agree with it. I had had non-human recognition since I was 3 or 4. But I couldn't sort out my 'nearly-true theriotype' until the adolescence stage. And when I could detect the accurate theriotype was later stage of 20's. It took a pretty long time.
@
Jeb_CC 's metaphor, identity is like a clay sculpture perfectly makes sense to me. Without accurate references, I cannot draw nice art nor good 3D models. I have to reference photos, anatomy, and actual animals to draw or model. Identity is just like that, I feel. We can imagine 'maybe something like this' without accurate reference, but cannot picture the detail unless we see the objective reference. Just like we cannot see ourselves without a mirror.
I personally feel, my identity can decompose into an amorphous, chaotic mud. It can shape into anything or anyone, but 'nobody' at the same time. Perhaps our subconscious is like that. What we're thinking 'ourselves' is the tip of the iceberg, this is a well-known theory in psychology. Potentially we can be anything or anyone but we're taking the shape of what we want to be or 'should be', willingly, necessarily, or forcibly. Perhaps the human brain has the potential to imagine like that, and it is the source of the creativity of humanity.
However.
For both good and bad in therian's case, we have the 'awkward gift' of being a non-human animal.
Just like dogs, our 'awkward gift' defines what we're good at and what we're not good at when we were born. Like working groups, herding groups, hunting groups, or toy groups, many dog bleeds are specialized for their use or purpose, have innate superiority in their own tasks on both their body and mind.
In my personal forecast, therianthropy is the phenomenon of 'sharping' our basic shape of an identity, which originally can be anyone or anything into specifically 'something non-human'. Still we can decorate our identities, yes. But the most solid core shape cannot be anyone or anything else, for good and bad. Or at least it has shape-memory traits. Even if once it took another shape or smashed, but eventually it returned to the original form. That is the difference between normal humans and us, at least I personally think so.
So both 'discovery and reference' and 'imagination and creation' are important elements to one's identity. Even if the basic shape is solid and unchangeable, but still we can carve the details on the sculpture to make it more beautiful.
Some dogs are superior to normal humans in some specific tasks and that's why there are guide dogs, police dogs, military dogs, and therapy dogs. As long as we can draw our true potential in the right place and right purpose, we may perform better. But it depends on our respective circumstances. So finding one's theriotype means finding their superiority in my opinion. Finding the most appropriate job which much to their theriotype is the key to drawing one's potential in my opinion.