A variety of reasons:
They were traditionally agrarian societies, so having a greater number of offspring meant that you had more hands to work in the fields.
After industrialisation came to the Indian Subcontinent, having a greater number of kids meant that you could send them off to work and they would earn money for the household.
Thus, economically, having a greater number of children was of immense benefit.
Culturally, the peoples of the Indian Subcontinent have always had a larger number of children than people in other parts of the world. Part of this stems from the fact that there's no system in place to take care of people in their old age. People in these countries remain dependent on their children late in life, and because most people live in poverty, it's believed that petering out the funds necessary for taking care of one's parents in their twilight years among a large number of siblings helps ease the burden on everyone.
Many people on the Indian Subcontinent live under an outdated and unfair class system. The practice of dowries is still a widespread custom, so like many places in Asia, there's a stigma attached to girls and a prestige attached to boys, thus making having a son far more attractive than having a daughter.
And because these societies have still not advanced to the standards of the developed world, many of these root causes persist in their societies today.
People in North America, Northern and Western Europe, Australia and New Zealand cannot afford to have large families if they wish to give each child a good life. Procuring housing for a great number of children, educating them and ensuring that they are given all of the opportunities possible is the top priority, so to do that, people in those regions have fewer children.
There are also vast differences in the population distribution across the Indian Subcontinent. Parts of India and Pakistan have an extremely high population density, but by world standards, both are large countries and there are also large areas where there are hardly any people. If you include Nepal and Bhutan as part of this region, you'd be including two countries that have a very different situation in terms of demographics, population and customs. Bangladesh is incredibly overcrowded, but it's far smaller than India or Pakistan. Sri Lankans live in dire poverty. The island is roughly the same size as Ireland, but has more than quadruple the population. The Maldives is geographically, politically, and culturally distinct, and while it's technically considered part of this region, it's really an anomaly.