The hostility exists for the same reasons that caused Pakistan be created and carved out of India. With the British leaving after several hundred years of colonisation and occupation, Muslims in India felt vulnerable to a Hindu majority state. They were fearful that the Hindu majority would ostracise, separate and subdue them. Out of that fear began the movement for the creation of a Pakistani state and for the creation of a sovereign Muslim state. This was agreed to by the British, who created West and East Pakistan, with East Pakistan ultimately becoming Bangladesh in the 1970s.
The people had become divided because of being colonised by the British for so long. Their own divisions had been exploited by their colonisers to such a degree that the country was ultimately carved into two states.
Suddenly there were two countries who spoke the same language, had similar customs, similar traditions but who saw each other as the consummate other. That ratcheted up an intense nationalism - even nativism - to a degree where each viewed itself as superior to the other and then could only see the other as an existential threat.
“Both countries are engaged in a game of hatred and vitriol that defies logic and reason.”
In that light, the idea that Kashmir is behind the dispute between Pakistan and India is a bit of a red herring. I think it's a convenient tool both militaries use to guarantee their survival. Pakistan is admittedly different because the military has repeatedly and routinely subverted the democratic process, becoming a dominant institution in the country.
So what happens now? In Pakistan, we've had both military dictators and governments who've been thrown out of office. But there are some some bright lights: we saw the first ever democratic transition of power in Pakistan four years ago and we are potentially looking at a second democratic transition of power. For a country that's 70 years old that's pretty important. But it's disheartening because the military is still the most dominant force. We've seen the government weakened in Pakistan by the military.
We've also seen dynamics change in India as well. Prime Minister Narendra Modi belongs to the BJP party. He is accused of what's been described as anti-muslim pogroms in the states where he was a leader, and for a very long time was barred from the United States and Israel. This anti-Muslim sentiment in India is very real - just like the anti Hindu sentiment in Pakistan is still very real. The only difference now is that these two countries are both nuclear-armed rivals as well.
I think the hostility really just boils down to the fact that these are really ultimately the same people who came from the same mother. They simply stopped seeing their similarities. And because of that they are engaged in this game of hatred and vitriol which really defies logic and reason. Bear in mind I've been to both India and Pakistan and, to me, the commonalities and the centuries-old history that they share are mind blowing.