The "war hawks" supported the war because of their desire to defend the young country's "national honor." which battle most supported their claim that the independence of the young country was at stake?

Here we are talking about the War of 1812. The term itself was coined during that period to describe the politicians who propagated the entry into war with Great Britain. The Burning of Washington D.C. in 1812 by Major General Robert Ross and his troops is the event here that supported the claims made by "war hawks".