But:
"The British had nothing to do with the partition.....Over 2,000,000 people died before the British negotiated a partition agreement"
So they kind of, sort of did have some hand in the partition, although it's true they didn't mandate it.
At that point, they just tried to mitigate the carnage. The factors driving partition were the arrogance of the Congress Party, which claimed to represent all Indians, and paranoia on the part of Muslims. They, rightly, saw Congress as Hindu dominated, though to be fair, it was not a religious party, more a socialist/anti-colonialist party, just completely dominated by Hindu elites.
The British, in the wake of WWII just wanted out, multiple attempts to manage the process collapsed due to both Muslim League and Congress Party stubbornness. With millions of people intermixed, there was massive displacement, continuous strife, and borders created that satisfied nobody.