Matangi and parrots are more than allegory 
There is a special 9-day festival called Shyamala Navaratri where I do this mantra chanting for 9 days and consume just milk and honey. For many years, nothing was felt. Now, I see parrots around our house all the time, just during those days, and then they are gone.
There are two main Goddesses - Kali who is death and Lalita who is life. Matangi is the only Goddess who is midway between the two. She destroys the unnecessary and sustains the necessary.
As Kali - she is called Matangi and represents the left-hand path
As Lalita - she is called Shyamala and represents the right-hand path
She is also one of the deities who communicates often in this day and age. She is called Mantrini - as she represents the power of speech which is the basis for all mantras. it is said that one who perfects her mantra gets success effortlessly in all other mantras.
She is the most complex archetype amongst Mahavidya Goddesses. I will write more about her when she permits me 
She is also the most sought after deity by politicians and movie stars in India because her rituals give victory, power, success, charisma, etc.
