What were the arguments of those those who claimed that we had "lost" China to the communists in 1949?

I am not completely sure which arguments you mean, so I will give you a few things that were said back then.  Your teacher probably expects to see something specific from your book or lectures, though.

The major argument they made was that China was ours to lose.  They argued that China was naturally our ally and that it should never have become communist.

A second major argument they made is that we lost China because the US government was too soft on Communism.  They argued that Democrats like those in Harry Truman's administration were the next best things to Communists themselves.  Because of this, they said, the government did not care if the Communists took China.  That, they argued, was why we "lost" China.