The argument does not follow:

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>We should believe only the truth. (premise)

If S should do A, then S can do A. (premise)

If determinism is true, then if S can do A, S does A. (premise)

So if determinism is true, then if S should do A, S does A. (from 2, 3)

So if determinism is true, then we believe only the truth. (from 1, 4)

I believe I have free will. (empirical premise)

So if determinism is true, then it is true that I have free will. (from 5, 6)

So determinism is false. (from 7)

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Just because you should believe the truth is does not mean you can only believe the truth.

This seems like a phrasing trick. By this logic you can justify any belief as true, determinism does not mean everything you believe is true.

This argument ignores that there is such a thing as a mistaken belief.