Oh it’s a long complicated history which is worthy of a niche and focus in history within higher education for example.

I suppose you could start at 1947 when Pakistan and India gained independence and even then depending on how you view it, you could claim that the British screwed both sides during the event furthering animosity between Hindus and Muslims in the region. The dream of a Muslim independent state starts at ~1857 when the Mughals who were primarily Muslim ruled over India for about a ~1000yrs lost out to the British which would then become to displace Mughals and rule over India and pillage it’s natural resources, not to say the Mughals weren’t guilty of their own set of atrocities. Again depending on how you look at, you could also consider Mughals invaders to a certain extent when they started gaining influence around ~700s with arrival of delegates of the Ummayad Caliphate and imposed themselves over a local populace that was primarily Hindu and Buddhist which existed in the region for 1000s of years prior with their own rich histories and cultures.

Forwarding back over to after the events of 1947, which lead to the creation of India and Pakistan and present day Bangladesh which was part of Pakistan as well. Bangladesh’s independence from Pakistan, 4 wars between India and Pakistan and regular skirmishes over the territorial dispute of Kashmir later, you have a very complicated and deep history influencing feelings for almost any individual that belongs to the region.

Largely, the people actually love each other and are fascinated by their similarities and differences in cultures, only to be manipulated by their governments for political favors and votes like any other region in the world.

Like all history, there’s numerous takes and narratives on any detail you can pick, so consider this as just one take of it.

Putting a note for further clarity just so we get things technically clear: “The Mughals” as in the actual dynasty didn’t rule India for a thousand years. It was Muslims and their presence in general. The Mughals were a part of the Muslim presence in India which shaped the subcontinent before the British came in.