You ought to change the "canonical" in your name to "comical".India will not back down, so China really has no choice other than either to push India into the Western camp or to compromise. It's really that simple. Given that China has bad relations with the entire developed world - US + Canada + UK + EU + Japan + SK + Australia, is it really rational for China to make another enemy with the most populous nation and the fastest growing major economy? I don't think so.
India is already in the Western camp. India spent centuries colonized by Britain so its present role comes as naturally as breathing to it. Don't pretend India has the power to make independent foreign policy choices, nobody here with two functioning brain cells to spare buys it.
China's "bad relations" with the West is entirely the West's fault. It's an unavoidable result of two immutable facts: 1) China's unstoppable ascent, and 2) The West's racism. Incidentally, India would have bad relations with the West as well if it were anything but a basket case. You have "good relations" with the West because the idea of India rising and threatening the West's hegemony is an absolute joke.
Fastest growing major economy? By how much does India's economy grow each year? In relative terms, it's nothing special. China grew at twice the rate when it was at a similar stage of development. In absolute terms, India's growth is barely a rounding error in comparison to China's growth.