Why would firing the joint chiefs of staff look so bad for jfk even as they defy his orders?

Because he did not want it to appear that the country's administration was in disagreement.

Explanation:

It is expected that all those who run the country will be in agreement with each other, if this is not shown to the public the government will show a weak appearance and the president can be seen as unprepared for the position. For this reason, Kennedy did not dismiss the heads of joint team, so that his popularity, as governor, did not stop due to rumors of disagreement between the members of the administration.

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