I'll like to comment specific on the USA, Pakistan, India equation on discussion in the thread.
Let us take the USA-Pak relations first.
To begin with, there is a historic background to it, Pakistan was specifically created because of its geo-strategic location, infact look into the history and the USA was against the idea of creating Pakistan, and it was the UK which was to sell the idea of a strategically important piece of land close to West Asia, Central Asia, Afghanistan, India and China, to the USA, and they were to take the bait. The idea was, if you control this land, you can further aim to control and dominate vast land from there. Look at the presence of the US in Asia, and you will get a sense of just how important Pakistan is to the American ambitions in the region. Remember, the core significance of Pakistan has not changed, be it for the Americans or the Chinese, it was about location back then and remains so today. Now, when Pakistan came into being, their ruling elite understood the idea of geo-strategic location and they sold the idea to the west, Jinnah to begin with, followed by the rest and till date.
The other thing, their being came with a fear psychosis of India either dismembering them or invading them and so they created a dependency syndrome which was first exploited by the west and the Islamic comity, and now by the west, Islamic comity and the PRC. The fear in parts true, initially Nehru was to write-off Pakistan and he didn't expect it to last for more than a decade, and later a joint effort by Soviet Union and India in 1971 which led to the creation of Bangladesh, and Pakistan has not been able to come off '71 till now. In order to have their back sides covered, the USA was allowed unprecedented access, the ruling elite got the handouts, and the mass was sold the idea of friendship, much like as is being done with the Sino-Pak relations. Now think of it, who would ever let go of such access and a country which is ready to fall head over heels for you, definitely not a super power, and another big power in making.
Now let us reflect on Indo-USA relations.
The Indo-US relations are on a very different pedestrial. This is a far more well defined and a more holistic relationship which incorporates defence, common threats, economy, space exploration, common strategic interests in Africa and East Asia specifically and other regions as well, as a matter of fact India's role has increased in the SEA region largely thanks to the USA, India getting access to certain high tables, the civil nuclear deal, oil and raw material exploration, and there ought to be more than mentioned here.
What we have to learn to do is to not see ourselves from a lens similar to how Pakistan perceives itself as, nor get into any zero sum games. Just because Pakistan has relations with someone, doesn't mean we don't work our relations with them. Pakistan has had very narrow vision all throughout its existence, and it never positioned itself to benefit its interests best. Unlike them, we today have a mature, functional, and a rational policy making, we have grown in economic stature, have a far more well-rounded foreign policy, we do understand what all needs to extracted from a relationship, most importantly, we have not positioned ourselves as a weak nation which is in desperate need of others, which Pakistan always has.
There is so much more to the Indo-USA relations than just the PRC, a skewed notion floated by an insecure PRC and Pakistan.
Important in foreign policy is not that you choose sides as per the whips and fancies of others, but you make them do that for you, for now our economic or the defence or diplomatic clout aren't anywhere close to do tha but we have forced the USA to change its policy towards Pakistan, but if we are believe they will ever let go off them for us, never is that going to happen, they can't have a better client state, so let us do our thing that benefits us and not bother too much on the USA-Pak thing.