What was the greatest concern of the authors of the federalist papers, preserving social liberties or ensuring national security?

They are afraid that making the central government weaker than the states could potentially cause division in the country and lead to secession.

Explanation:

At that time, the initial draft of the constitution give the central government with very little power of the states. For example The central government was unable to collect taxes from the states, they were not free to mobilize military force to the states, and the federal government's law do not have supremacy over the states' law.

The authors of the federalists believe that this will cause a lot of problem in our country.

Examples of threat to social liberties :

if one state decided to conduct a massive discrimination to a certain group of citizens, the central government will have very little influence to stop it .

Examples of threat to national security :

The central government would't be able stop the states from conducting businesses with other countries that they consider as rival.

answer; a cost benefit analysis;