I am not a historian. I am merely someone who has studied this topic, thought about it and discussed it at length. I will provide my sources towards the end. This is also my first answer on this subreddit, so if it does not meet the standards of the subreddit, I am ok with it being deleted.

To understand the situation in India in 1947, one must go all the way back to the 19th century (and also beyond). By the 19th century, India had been under Muslim rule for 700 years. Now, just saying that the Rulers of India were Muslim hides more than it reveals because a significant portion of the Ruling Elite were Hindus. Yes, the Mughal Emperor was a Muslim, and so were all his Governors and most of his Military Generals. However, many ordinary office bearers were Hindus, the Rajput Kings (From what is today Rajasthan) were all co-opted into Mughal rule with many of them rising to high ranks in the Mughal Administration. These Rajput Kings were Soldiers, Administrators, Financiers and more. They were as enmeshed in the Mughal rule as a Muslim chieftain. The Marathas (from what is today Maharashtra), most of them peasant warriors, first served the Muslim Sultans of the Deccan, and then the Mughal Emperor before breaking away on their own. Even in 1773, when Maratha Power was at it's height, the Scindia (The Maratha Chieftain closest to Delhi), acknowledged Shah Alam II as the emperor of India and paid tribute to him. The rulers of India were Muslim, but there were many Hindus who were part of the ruling and administrative elite. Coming to the common populace, if the population of what is today India, Pakistan and Bangladesh were taken together, the Hindus were the majority community with a significant minority being Muslims. However, there was no concept of majority and minority. This is important because the Muslims (and certainly the elite among them) viewed themselves as the Rulers of India. They did not view themselves as the minority community at the whims of the majority Hindus. The Hindus too, did not view themselves as the majority oppressed by the minority. While Hindus and Muslims lead, by and large, separate social lives, they were enmeshed economically and politically. Such was the situation in India in the early 19th century.

All of this changed when the British came to power in large parts of India. When they first came to power in the late 18th and early 19th century, the traditional systems of Government in India had broken down. The once mighty Mughal Empire was nothing more than the environs of Delhi. Most of Northern India was in chaos. The British set about reorganising the Government in their own image and set in place a colonial administration mirroring that of Britain. This Government was staffed by Englishmen at the upper echelons, but the lower and middle ranks were Indians. English became the language of administration (Until 1835, Persian was the Lingua Franca of India) and Western, Secular education was introduced to produce candidates who could staff this administration. Upper caste/class Hindus took to this education in droves. Throughout the 19th century, the Muslim community did not take to this Secular education as much and remained cut out from the lower ranks of Government. Additionally, sections of the Muslim ruling elite (primarily the Mughal Emperor and his extended circle of courtiers) played a significant role in the Revolt of 1857. Thus the British viewed the Muslim community with suspicion and excluded them from the administration. Another development in the 19th century was the introduction of the census. The colonial administration wished to count and categorise it's subjects and carried out the first census of India in 1881. For the first time, ordinary people discovered that the Hindus were the majority community and the Muslims were in a minority. You must understand that until then, the Muslims were never conscious of the fact that there were many more Hindus than Muslims. It was taken for a fact that the Muslims were the rulers of India. But here was a situation where the Rulers were an alien people, from outside India, who favoured not them, but the Hindu majority. The Muslim community, for the first time, felt insecure and conscious of the fact that they were a minority. There was also little to no National Consciousness. The concept of a people called Indians was not extant as it is today. The Punjabi was different from the Bengali was different from the Tamil was different from the Maratha. They were, to use British terminology, "People of India", but they themselves did not think of themselves as Indian. India was not yet, a Nation.

By the end of the 19th century, Nationalism had started to pick up steam in India. The first shoots of the Independence movement had started to sprout. This was mainly lead by Hindu elites in the form of the Indian National Congress (INC). The first meeting of the INC was held in 1885 and by the first decade of the 20th century, the INC was making significant progress towards becoming a mass organisation that advocated more involvement for the natives in the administration. The INC was mainly composed of Hindus (though there was many Muslims who saw themselves as Nationalist Indians) for they were the initial takers to Western, Secular education and they were most influenced by the currents of Nationalism and Liberalism that were running through Europe. They were also secular in their outlook and did not view themselves as a movement for Hindus only. They strove to build a National Identity as Indians When the INC started to win concessions from the Government, the Muslim Elites started to get worried. They feared that the Hindu elites would corner most of the benefits of power and the Muslim elites would be shut out. This is evident from their demand for separate electorates for Muslims and a status in Governance mirroring that of the Muslim community a 100 years prior. The Muslim League was formed by these Muslim elites in 1906 and began to push for safeguarding of their interests and privileges. The position of the Muslim League was that the interests of the Muslim community in India was served only by the Muslim League and they (the League) were the sole representatives of the Muslims. The INC refused to concede this point and claimed to serve as the representatives of ALL Indians regardless of religious affinity.

Throughout the early 20th century, the Independence movement picked up steam and by the late 30s, some form of Independence was seen as inevitable. The INC, by this time, was truly a mass organisation with branches across the length and breadth of India. When India became independent, there was no doubt who would be in power. The League, in response, ramped up their rhetoric that Hindus and Muslims were two separate people and one could not live under the other. The British too, played off the Muslim League and the INC against each other. The Muslim League, which was a party of the elites initially, became a mass organisation as well. The "Two Nation Theory" gathered steam and attained a life of it's own. The Two Nation Theory argued that Hindus and Muslims were two separate people and had very little in common. It was put forth by the Muslim Elites to safeguard their power and authority. It became a mass movement that lead to riots and killings such as Direct Action Day in Calcutta on August 16th, 1946.

By the end of the Second World War, Britain was ready to grant independence to India. However, the INC and the Muslim League were unable to come to terms on power sharing. The situation in India was fast collapsing and Britain was desperate to extricate itself from an ugly situation. The solution was to partition the subcontinent into the modern nations of India and Pakistan.

My sources are as follows:

The Anarchy: The East India Company, Corporate Violence, and the Pillage of an Empire & The last Mughal - By William Dalrymple

India's Struggle for Independence: 1857-1947 - By Bipin Chandra