But India was an ally of the Soviet Union (and is still an ally of Russia), and so using the adage 'the enemy of your enemy is your friend,' and maybe a corollary 'the friend of your enemy is your enemy' for both Pakistan and India, can see where the government was figuratively coming from.
Whats you and most Americans forget...... the adage applies both ways. Pakistan was an ally of the US ..........and still is. Which is why US came to their rescue.
Remember well, the term, 'ally' isn't in the same as in the usual context. India never is, and never has been, an "ally" of anyone except herself. Tell me one base in the vast Indian expanse, that's operated by a foreign power?
As for the US, India did have a decent relationship with the US for most of the time, if not all. India even sponsored spying missions with the US against China, at a time that India was also the closest with Russia.
The Russian relationship was out of sheer necessity. The US wasn't willing to support a post-Independence India that seemed too large and too unstable compared to Pakistan (a big folly to assume) and they even prevented the British, who have always been key weapons supplier to India from selling advanced jets. That was the time when the Russians stepped in with offers of not just selling planes, but even establishing manufacturing lines for them, in India. It was an offer that was too hard to refuse. Besides, the Russians even helped the Indians drive off the USS Enterprise that had maintained a threatening posture off the Bay of Bengal, against India, in the 1971-72 Indo-Pakistan War.
And after all that, not a single Soviet base on Indian soil. So much for "alliance".
“But India was an ally of the Soviet Union (and is still an ally of Russia), and so using the adage ‘the enemy of your enemy is your friend,’ “
There is a flaw in that logic. The enemy of your enemy may actually also be your enemy. As you can see in this situation, the friend(India) of the enemy (USSR) was also a friend of a friend(Israel). And the so called friend (Pak) was also the enemy of a Friend (Isreal).
This is how life is. Maybe US needs to learn to think more.