C.
This is why we have good relations currently.
A third party is a part that doesn’t fit the criteria of belonging to the two dominant parties of the US. In simple terms, it is any party that isn’t the two dominant parties (republican and democratic).
Firing the joint chiefs of staff would look bad for Kennedy because it would make it appear to the public that the administration is struggling/weak. Anytime there are scandals or issues in which the president does not get along with his colleagues, it is seen as a sign of weakness. During Kennedy's presidency, the last thing the United States government wanted was to appear weak. This is because the US was in constant competition with the Soviet Union for international power and influence.