The way we work together in your voice lessons is basically this:
I give you an exercise to sing. You sing it, as spontaneously as possible, doing your best not to interfere with the reflex response of your voice. I listen, evaluate the results, and carefully choose a next exercise to exploit any successes while correcting any problems.
In this process, we both have firmly differentiated roles, requiring dissimilar mindsets.
I need to be in an analytical mode, since I have to judge what is going right and wrong in your vocal coordination based on the sensory information coming to my ears and eyes.
In order to sing with the freedom required in these exercises, you need to be as free as possible from judgment of the results of your singing. Self-judgment stifles your spontaneity, making it more likely that you will gravitate towards the familiar, rather than the new and potentially better. Only when you are not concerned about the result can you properly focus on the process you are undertaking to produce it. (This is similar to that sought-after Zen state of being in the moment, focusing on means rather than ends.)
The upshot is that my way of vocally working with you requires one of us to be a judge and one of us to abstain from judgement. If you tried to replicate this process on your own between lessons, you would have to simultaneously judge and abstain from judgement, clearly an impossibility!
There are more productive uses of your practice time than to try in vain to be your own voice teacher. I suggested some in another post yesterday. If you want more ideas for self-study, feel free to ask me in your lessons.