Allow me to present some history about the man before we continue.
Jinnah joined the INC in 1904, a decade before Gandhi was anywhere on the INC's radar. He was the member of the moderate faction of Congress which advocated for hindu-muslim unity and self-rule through constitutional means. He even wrote a scathing article criticising the founding of the Muslim League in 1906.
By the time the First World War rolled in he had joined up, along with his allies in the moderate faction, with the radical faction of INC and formed the Home Rule Movement. They were seeing some success but then the war put any ideas for reform on the back burner. It was at this time that Gandhi showed up in the picture. In the meantime in 1912 order to secure a entente he joined the Muslim League. He did not leave the INC until much later.
By 1919 most of Jinnah's allies in the moderate faction had died. This had severely weakened the Moderate faction. Gandhi meanwhile used this vacuum to bolster his influence on the INC. He used the Khilafat movement which for the reinstatement of the Ottoman Emperor as the Caliph of all (Sunni) Muslims as a springboard to gaining support among the muslims. His idea of satyagrah really caught on with the enraged nation in the aftermath of the Jallianwallah Bagh Massacre in 1919. Jinnah believed the satyagrah movement under Gandhi to be counterproductive as it would further alienate the British government, and make them more unwilling to accept change, both of which it did. At this point he was shouted down in the INC meetings and Jinnah had finally lost all influence in the INC. In 1920 he finally resigned from congress.
Then spent a good part of the next decade and a half in the wilderness. It was finally in 1933 that he decided to step back into the political ring to contest the elections in provincial 1937. The Muslim league got soundly drubbed and won few seats, even in the Muslim majority regions. The INC even won the majority of the seats in modern day Waziristan in Pakistan where virtually the entire population was Muslim. [1]
This made him rethink his strategy and dramatically expand membership of his party. As such the Muslim league was perfectly poised to step into the political vacuum created by the arrest of Gandhi and Nehru in 1940, just as Gandhi had before him; and take his party from the fringes to the center stage.
Now moving on to actually answering your question as to the cause for the divide.
Well starting off in 1914 itself Jinnah was convinced that Gandhi's movement would only lead to chaos (which it sort of did ref: Chauri Chaura incident) and would lead to an alienation of the British government from the Indian movements. He was a lawyer, like Gandhi. Unlike Gandhi he wanted to work with the system not break it down.
Also there was the issue that Gandhi basically came into the picture a lot later than Jinnah and showed him the door. Gandhi basically proceeded to dismantle everything Jinnah had worked for (i.e., the rapport between the moderate faction of the INC and the government) and remove any opposition in the INC, which included Jinnah and his supporters. I wouldn't be surprised if all this made Jinnah feel Gandhi was an usurper.
Towards the end of this story Jinnah was convinced that Gandhi was turning the INC into a mouthpiece. Gandhi had successfully sidelined many of his opponents within the INC starting from Jinnah and the emaciated Moderates and later the radicals like Subhash Chandra Bose. In the later case he openly demanded that Bose step down or that Gandhi would go on another hunger strike to the death (his preferred weapon). The machinations of the Gandhi Clique made Jinnah wary of association with him.
His support for the formation of Pakistan came from the fact that his suggestion to the INC for securing the Muslims in a Hindu majority India were not acted upon several times. When he took over the Muslim League in 1929 he realised that this was his ticket to establishing a party that could take on the INC, and by extension the Gandhi clique, and the virtual hegemony it had on Indian politics.
Gandhi meanwhile had started moving from a secular ideology to an ideology for his movement based on certain ideas of Hinduism. This was so as to secure a larger support base among the Hindu masses. Obviously this was threatening to Jinnah who knew that if the independence movement went down that route, there would be lesser political guarantees for Muslims in independent India.
Meanwhile soon after his release Gandhi expressed deep discontentment with the idea of Partition. He had rightly foreseen that it would lead to needless blood shed. Unfortunately for him, Jinnah was convinced that it was another on of his ploys to manipulate Jinnah into submission. That combined with the favouring of Nehru as Gandhi's right hand man sealed off any avenues for rapprochement between the two camps.
So that was what finally galvanized him to action and convinced him to push for Pakistan. By 1941-42 the idea of Pakistan held widespread appeal among Indian Muslims and the Gandhi-Jinnah split was irreparable.
And this is how Gandhi the man responsible (inadvertently so) for the partition of the subcontinent is known as one of the staunches opponents of partition.
And Jinnah one of the most eloquent and erudite voices in the Indian independence movement and for Hindu-Muslim solidarity became the architect of the Partition.
Hope this helps.
[1] Interestingly enough modern day waziristan is the place where most of the ISI funded terrorists camps are. It basically the lawless badlands of Pakistan.