Hi Anu,
Though I don't want to argue in this matter, still I think Indian culture has given more importance to females. "Vande Mataram," "Mother country," "Mother land," "Mother tongue," etc. represent a female-dominated society. "Sita-Ram," "Radhe-Shyam," "Uma-Shankar," "Gouri-Shankar," "Lakshmi-Narayana," etc. all represent females first and then males. In ancient times, the three major powers - Finance, Knowledge, and Armaments were symbolized by goddesses Sri Lakshmi, Sri Saraswati, and Sru Durga, respectively, all of whom are female.
On the other hand, foreigners say "Father Country," and the English word "History" comes from "His+story." Therefore, in my opinion, Indian culture cannot be blamed for using the term "bhai-bhai."
Regards,
Anu