Why is it a problem if China starts "dumping" US Treasuries? What does it mean to be dumping? China has 1.2 trillion dollars worth of us treasuries. Why would it be a problem for them to get rid of all of them? Why would that destabilize the US economy?
It would increase the total supply of US treasuries available at any point in time, which would require a higher interest rate for the market to clear. Higher interest rates would increase the cost of capital in the US economy, which in most conditions will reduce investment.

However, higher supply would also decrease the exchange rate of the USD, which could be beneficial for exports (which needs to be considered in a context of higher cost of consumer imports and higher cost of production inputs).

"Dumping" would be fine as a descriptive word for many informal contexts, but "dumping" has specific meaning in an international legal context, such as in the WTO, and so regarding the specific question of what it would mean to unload large volumes of US treasuries at the same time, e.g. for the purpose of negatively impacting the US economy, "dumping" would not be the correct term.

It should also be mentioned that China would immediately lose significant financial assets if the 1.2 trillion in treasuries were to lose 100 billion or 200 billion dollars in equivalent value. Considering the relatively large volume of credit extended in the Chinese economy relative to financial assets, this implies a relatively major economic cost to China if it were to make such a move. On the matter of strategic reasons to hold large volumes of US treasuries, the face value argument of the Chinese government is legitimate, if not the complete story: What else should they be holding if not US treasuries?