Defense secretary Leon Panetta urged India to take a more active role in Afghanistan as international forces there draw down after more than a decade of war, American officials told the Reuters news agency on Tuesday when the Pentagon chief was due to arrive in New Delhi for two days of talks.

The Americans recognize that the longstanding rivalry between India and Pakistan will be an obstacle to peace in Afghanistan once their soldiers have pulled out in 2014 but, “This is not predestined,” said one official. “This does not have to be the case.”

Well. It may not be predestined but to suppose that India and Pakistan will suddenly work together for the first time in their independent histories because the United States would like them to is overly optimistic at best.

Indo-Pakistani rivalry is not some petty political dispute. It is a struggle for regional influence and grounded in Pakistan’s sense of insecurity. Afghanistan is an integral part of that.

For nearly ten years, America asked very little of India in Afghanistan because it recognized that doing so would antagonize Pakistan whose support is critical to combatting the Islamic insurgents on the Afghan-Pakistani frontier.

Now, with American-Pakistani relations so strained, there is little hesitation in Washington to embrace India as an ally. Senators have openly encouraged New Delhi to “to fill the vacuum in Kabul once we leave.” It helps that India is also expected to balance against China’s rise.

India’s efforts in Afghanistan stem from a determination to reestablish the pattern that prevailed from 1947 to 1992, wrote Rajan Menon wrote in The American Interest last month, “when Afghanistan was ruled by a series of regimes that, while different in makeup, were all friendly toward India and wary of Pakistan.”

The configuration changed to India’s detriment once assorted anti-Soviet mujahideen groups began a vicious battle for power that year. That melee enabled the Taliban’s rise in 1994 and, with support from Pakistan’s military and intelligence services, its victory two years later.

Pakistan subsequently enjoyed “strategic depth” in Afghanistan which it has tried to regain since the American invasion in 2001. As Menon put it, Pakistan’s military and intelligence services are quite resolved “to counter India’s flanking maneuver and to establish a dependent government in Kabul.”

Unlike the American officials speaking with Reuters, Menon has no illusions about how both countries will react to an American withdrawal. “Neither India nor Pakistan will be able to resist the temptation to exploit each other’s weaknesses in other locations once their contest in post-American Afghanistan accelerates,” he writes.

For Pakistan, the most likely venue is Indian Kashmir; for India, it is Balochistan, Pakistan’s poorest province, home to a third of its natural gas as well as other resources and the site of an armed rebellion that has persisted with varying intensity since 1948, prompting major military offensives by the government.

That is what the United States will be leaving behind — an Indo-Pakistani struggle that is only intensified and will inhibit India’s ability to act as a bulwark against China in the Indian Ocean region. As much as the Americans may like the bend the arc of Indo-Pakistani history, the geopolitics of South Asia are likely to prevail.