To answer your question, we must look at what the imperatives were for the various stakeholders in the complex task that was Partition.

For such a monumental task, the question of how partition was actually going to be carried out was decided in a relatively brief span of time. From the British standpoint, the decision to grant independence to India, in whatever form, happened in late 1945 after the Labour victory in the general election. That's barely two years prior to independence in August 1947.

The outcome we see today of two states, India and Pakistan (+ Bangladesh, but thats another story) wasn't guaranteed from the start. Right from the start of negotiations, several options for the future of the subcontinent were put on the table.

In March 1946, a British proposal put forward the idea of a federation of Hindu and Muslim provinces under the leadership of a (relatively weak) central govt. Under this plan, Muslim provinces were to be given significant autonomy within a united India, and united administratively so as to give the Muslim population enough weight in a Hindu majority country. Above all, Jinnah wanted to avoid what he called in 1944 a 'maimed, mutilated and moth eaten Pakistan' split by 2000km of a potentially hostile India.

The weakness of the central govt under this plan put off Congress's leaders who torpedoed it in July 1946. By that point, time was running out. Civil disruptions and interethnic violence (eg. The Calcutta massacre, Aug 1946) meant that a solution needed to be found quickly lest the subcontinent descended into an uncontrollable civil war.

In response to the worsening situation on the ground, Mountbatten was appointed as vice Roy in Feb 1947 with instructions to transfer power before June 1948 at the latest, in whatever form. Under immense time pressure to come up with a solution, Mountbatten and his staff had to answer several crucial questions, all while representatives of India's princely states, linked to the Crown by pseudo vassalic ties, demanded guarantees from the man who would decide the fate of their polities. By the time he came along, a united India was out of the question. Mountbatten initially proposed transferring power to the various provinces and princely states, who could make one of three choices: (1) Join Pakistan (2) Join India, or (3) stay independent.

Nehru categorically refused this. Just as Jinnah detested the idea of a 'moth-eaten' Pakistan, Nehru loathed the thought of the balkanisation of the subcontinent into various states. Soon after Mountbatten took office, Nehru convinced him to hand over power to two successor states only, with no option for independence.

The modalities of independence were decided: the Raj would be split into two dominions, with the princes being left to fend for themselves and negotiate directly with the new governments who, intent to avoid a balkanisation of the subcontinent, were determined to bring about their integration. Many princes tried to plead for better terms, but most, ruling only very small territories, held little leverage over the powerful Indian government. These princes were only bound to the British Crown, not to the govt of the British Raj, and Mountbatten, eager to limit his country's involvement in the crisis, insisted that the princes could expect no assistance from Britain

Most princely states were integrated relatively quickly thanks to the decisive work of Vallabhai Patel and VP Menon, who brought the princes into the fold through a combination of threats, intimidations, and promises of lush privy purses.

Most, except the elephant in the room, Hyderabad. The Nizam ruled over a large and populous state that sat right in the middle of India. An independent Hyderabad state was not a viable option from the start. Firstly, the Indian govt was, as we mentioned, hostile to the idea of breakaway states. Especially so, in the minds of Patel, as Hyderabad had a Hindu majority population ruled by a Muslim ruler, and therefore could harbor sympathies for Pakistan (like the Maharaja of Janagarh in present day Gujarat who attempted to join Pakistan). Secondly, Hyderabad was landlocked, and if independent would be surrounded by a hostile power intent on conquering it.

Nehru and Patel were not going to let a potentially hostile state be independent right in the middle of their own, creating a "moth eyed India" to mirror Jinnah's words. In the end, they ordered the Indian army to march into Hyderabad and forcibly annex the state in September 1948.

Sources:

Barbara D. Metcalf and Thomas Metcalf, A Concise History of Modern India (Cambridge: Cambridge University Press, 2006)

Ian Copland, The Princes of India in the Endgame of Empire (Cambridge: Cambridge University Press, 1997)