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Mohandas Karamchand Gandhi (MKG) viewed the world from Vegetarian-Gujarati-Baniya glasses. These glasses however partial they are, are purely indic in origin. So in other words, contrary to many other senior INC leaders (Except Tilak, Lajpatrai and Bipinchandrapal), he had the world-view and the empathy to connect with rural masses of India beyond Western Maharashtra, Southern Punjab (around Lahore), and Urban Bengal. Gandhi's attire and way of reaching out to people made them feel responsible towards a national cause. The efficacy of Satyagraha on India's independence is a shoddy cover-up. But what cannot be denied is that, he awakened the dormant rank and file of Hindu society from 1920 to 1939. This awakening of Hindu society in these twenty years of Gandhi is mark of sheer genius. He found the pulse of Hindus and could project the control over that pulse many times at will over large and diverse Hindu population.
He made available a safe way for a Hindu man to contribute his tiny bit towards a national cause and raise his political awareness. The rise in the political awareness of mango Hindu is perhaps one of the single biggest contribution of MKG for mother India. Typically, a Muslim had a higher political awareness than a Hindu of national and particularly of international politics. A Muslim abdul going to madrassa will know about Turkey, Istanbul, Jerusalem, Rome, Mecca-Medina, Egypt, Baghdad and related stories. The phrase of Room-Shaam (from Rome to Siam) is made popular in Indian languages after the influence of Islam. A Hindu showed lesser awareness of international and national situation (at least places) except for popular pilgrimage places. The Polity is inherent part of Islam. In Indic religions, Artha is segregated from Dharma and Moksha (which is what pilgrimage is about).
The glasses gandhi were Indic. This was a totally Indic way of looking towards polity and Indic way of mobilizing masses for a particular cause. I am not saying this is the only way, other way is that of Shivaji and Govindsinghji. However, in given times, he was the only one to have both a unique "hindu" world-view as well as empathy of the masses. This is where Bipinchandra Pal and Lala Lajpat rai could not compete after death of Tilak. These three had the world-view similar to Shivaji and Govindsinghji. Tilak had both but his age was against him. And Tilak's political and ideological heir, Veer Savarkar, lost out precious years in imprisonment at Andamans.
These Vegetarian-Gujarati-Baniya glasses of MKG were the source of his greatest strength and greatest weakness. He looked at everyone through these glasses. These glasses of him enabled him to feel the pulse of 80% of Indians. But this made him totally disconnected from remaining 20%, the Indian muslims. He viewed IM from these glasses too, and this is what led to his undoing. Starting from Khilafat, he continuously misunderstood Islam. His conviction and his successes with Indian Hindus made him callous to the warnings of others who understood Islam, including the warning of Muhammad ali Jinnah while his opposition to Khilafat movement in 1917. He tried to control and pamper them as he pampered and controlled the "harijans" or the "Dalits" of hindu society.
His personal integrity and purity of character is comparable only to a Rishi. However, only Hindus venerate chaste Rishis. The saints of Muslims and Christians are proselytizing warlords who are proficient at killing or converting the heathens (St. Xaviers, for example). He totally misunderstood this part.
Hence the statement - MKG understood Hindus more than anyone else in his times, and he repetitively misunderstood Muslims more than anyone else in his times.