Your co-worker is both correct and incorrect.
In a file server system, a significant amount of data/information is copied to the client. Why? Because the client is where the work must take place. This differs from a client server system in which work is capable of being done and is done on the server.

He is incorrect to the extent that this is bad. Sometimes it is bad. File server systems for the most part do not scale. But often, the issue is not material.

So, to the argument question, as far as the nature of what file server systems are and how they accomplish their work, there is not much to say there. It is a statement of fact. There is no counter-argument available to you.

With respect to the argument of whether it is good or bad, and this by the way is your real argument, there is no one right or wrong answer. Not knowing the specifics of your scenario, it might be bad, it might be OK.

For sure, it is not fair to make a sweeping statement that it is always bad.