From my understanding (and please correct deficiencies!) is that the British switch to paper cartridges that were greased was believed to be an attempt to attack the religion of the populace, as it would require a soldier to essentially consume either beef or pork (offensive to Hindus and Muslims respectively). The local Company men were aware of this problem, and took steps to avoid this problem by altering drill and using non-greased cartridges that the soldiers were to grease themselves. Rather than solve the problem, this seemed to convince the mutineers of the original intent. To me, absent other provocations to the religion of the natives, that doesn't seem to make a lot of sense. So what had the British done to that point to get to that level of distrust?
Lots of reasons.
Nearly 2 decades of continuous fighting. These were not colonial rebellions. These were big wars against large countries. With attendant casualties. For instance during the Anglo-Sikh Wars, at Chillianwalla, 6 British regiments lost their colours, more than in the entire Peninsula War.
The increasing rate of war, meant soldiers were committed to fight outside India, in Persia, Japan, Afghanistan etc. Which led to disquiet.
Long campaigns meant deaths of officers who had served for years with and knew the soldiers. They were replaced by wet behind the ears toffs from the UK. Who handled indiscipline badly.
Political changes in India. Most of the soldiers were recruited from Bengal and surrounding regions. Especially Oudh. When Oudh, which had been an ally of the UK, was annexed under the Doctrine of Lapse, this led to great resentment.