Suppose I have an HD public xpubkey and I derive bitcoin public address(es) from it.
Given one of the public bitcoin address derived from it e.g. 1F1tAaz5x1....
Can you get the xpubkey e.g. xpub6DKUi1BvKEgn...
I thought it is impossible, but someone I know claims it is possible.
And if it is possible isn't the privacy compromised in this situation?

Not sure if this is directly related but also take a look at
Deterministic Wallets, Their Advantages and their Understated Flaws ("An Understated Problem" section):
https://bitcoinmagazine.com/articles/deterministic-wallets-advantages-flaw-1385450276/