I'll answer this to the best of my ability. This is a controversial issue, and it's hard to be completely neutral but I do my best to only present the facts.

To start, you need to understand the nature of British rule in the subcontinent. The British ruled India through a patchwork of directly controlled land, and princely states ruled by local nobility with British oversight. Kashmir was ruled by one of these princely states. The rulers of Kashmir were Hindu, though the majority of Kashmiri people at the time were Muslim. Though contrary to popular belief, it did have a notable Hindu population too. When the British were exiting the subcontinent, these princely states had 3 real choices, to join India, Pakistan or remain independent. The maharaja of Kashmir was leaning towards the independence option, despite a significant part of the population wanting to join Pakistan. Pakistan would eventually begin arming rebels and imposing an economic blockade, eventually launching a full invasion of Kashmir. India would only step in if the maharaja of Kashmir agreed to join India. He agreed to this offer and India sent troops to Kashmir.

India and Pakistan would have their first war over Kashmir, and from there, the conflict would only deepen. There would be more war, an exodus of most Kashmiri Hindus at the hands of pro-pakistan militants, civil unrest and more until we get to modern times.

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I didn't go into every single event to happen, but this should give you an idea of why India and Pakistan fight over Kashmir.