The major reason for this was the fact that the Muslim population in what is now Pakistan and the Hindu population in what is now India were unable to figure out a way to live together in one country. This, naturally, led to the idea that the two areas should split from one another and form different countries.
Please note however, that it was not the British who first came up with the idea of separate countries. This idea had been in existence from at least the early 1900s. Muslims such as Iqbal did not believe that they could truly be an equal part of a country that was, in their minds, dominated by Hindus. For this reason, they started to suggest the idea of partition. It is true that the British created the commission that drew the boundaries and it was Parliament that passed the law creating the two countries. However, partition was not an idea that was originated by the British.
The British thought that anymore delay would result in a civil war.