Why does Ramana Maharshi say there is no "other"?
My educated guess is that a particular seeker needed to hear that at that moment to shake him/her off the wrong belief that the person is a separate entity. And by doing so release the seeker from psychological suffering and establish the seeker in Impersonal Stillness.
There is no separate “I” entity. Neither for the sage nor for anyone else. Therefore the other” is a concept like “I” is. Useful and necessary for practical and functional purposes. Irrelevant and obstructing in terms of Self-Knowledge.