I have heard different theories like her mother was a cat demon, she has a kudo no one else has, or the cat is a really advanced gigai. I would really like to know if any of these are true and if not what is the real explanation for it?
There is no definitive answer to this and any attempts at an to answer this would be speculative at most. It was never explained in neither the manga nor the anime.
From the wiki:
...While it is unknown how she obtained her cat transformation, she appears to prefer spending most of her time in it....
It is never told why she can do this. But it has something to do with her leaving the Soul Society. It might have been the only way she was able to get out. She was the form of a cat for 100 years. She is the only known one to be able to do this.
Hope this helped!