It is important to understand there is some truth in the statement, while it neglects the symbolism that Hong Kong citizens have rallied behind.
It is no longer important, but the possibility of extradition to mainland China was a very small part of the bill, which updated a long list of countries that extradition would be possible to. It also lowered the number of crimes that were extraditable.
So on its face it was a meaningful updating of an old law and mostly kept the existing process which was full of appeals and approvals of various departments to actually extradite someone, but the mere inclusion of one particular country allowed everyone to channel their disdain for crossing an ideological line.
So when the first protest happened, China's cherry picking of the issue is not at all inaccurate. Coupled with the understanding that all the disdain comes towards them, from their own autonomous region, it is pretty embarrassing.