Partly, as a pretentiously iconoclastic radical secularist, I was suspicious of a national liberation movement led by the Dalai Lama, who I saw as basically a huckster (I also hated Mother Theresa, Archibishop Desmond Tutu and Gandhi. I'm no longer sure which ones of those I was right about), and suspicious of the filthy rich Buddhists who led the campaign from the West, such as Richard Gere. That was, to me, sufficient cause to differentiate myself from it.
Probably more significantly, I saw the support given to the movement (which was very fashionable then, probably second to the anti-apartheid movement in being generally accepted as right-on) as an easy option, because it fit in so well to the anti-Communist Cold War ideology that was dominant in the Thatcher/Reagan era.
I now diagnose this dismissiveness as part of the Stalinophilia that afflicts much of the left, even in its ostensibly anti-Stalinist varieties. By Stalinophilia, I mean the worldview that sees the Peking and Moscow families of state socialist regimes as bulwarks against the "real" enemy, Western capitalist/imperialism, and therefore, despite their evident evil, worth supporting (albeit "critically").
I am ashamed of that.
***On Tibet, meanwhile, read this great post at Flesh is Grass. And a slightly different view from the Jura Watchmaker.
P.S. Today's version of this Stalinophilia, of course, is Islamophilia, the idea that political Islam should be supported ("critically" or not) because it is the enemy of the "real" enemy, Western capitalist/imperialism.
Image from the International Campaign for Tibet.