We should be trying to get rid of antiquated or unnecessary military technology in order to help our country be more financially solvent. However, the USA has a bad track record of selling or giving away weapons and then regretting the decision. Selling weapons to a foreign country could look unfavorably on the US by different countries or could be used against us at some unforeseen time.
In my opinion there is no reason for the United States to ever sell advanced weaponry to other countries, and the F-16 fighter jets certainly falls into this category. Even with the economic interest inherent in selling these kinds of items, I think that it is for the best not to encourage violence, when possible.