what does "ego dance"mean?

In reading a book, i found the following paragraph:"For several minutes, we did the ego dance, with me trying to find an opeing in her frightened mind to allow her to approach the situation in a new way, and her struggling to convince me why it wouldn't work."

I looked up the phrase "ego dance" on the internet or all the dictionaries i can find, still i cannot find the meaning of this phrase.
Many Thanks!