Why does the US sell arms to Pakistan rather than India?

It is not that America doesn't sell to India. But India buys more from Russia.

After Indian independence (in 1947), India along with a few other nations started the non-aligned movement. They neither aligned with the USA bloc nor with the Soviet bloc. (Hence the name, "third world", which is now used with a different meaning).

USSR at that time helped India a lot in developing the education system and in science and technology. So despite India not officially in the Soviet bloc, was closer to USSR. India thus sourced most of its weapons form USSR. In all Indo-Pak wars, USSR supported India and USA supported Pakistan.

On the other hand, US always supported Pakistan. The "official" (or most widely accepted) reason is that it was to counter balance India's relation with USSR. USA gave financial aid to Pakistan. And Pakistan started buying most of its weapons from USA.

There is another reason which is given by some scholars but is not widely recognized. It is that the partition of India/Pakistan itself had its foundations in providing Britain/USA bases near Afghanistan to counter balance the Soviet threat in Afghanistan. They have provided some evidence that a lot of funding was provided to Jinnha and Muslim league (before independence of India) to press for partition. As India would never them bases. But creating another country at the north-west frontiers of India with Afghanistan.

After economic liberalisation of India in 1991, it started to become a major economic player globally. So USA also started friendly relations with India. Now India also buys from the US. There was a nuclear deal between India and US recently.

Pakistan is a Muslim country, India is Hindu, Buddhist, Christian and others. Obama/america only supports Muslim countries.