Father and son name two distinct human subjects, while cause and effect primarily express a relation of dependence. Not every feature of these analogies applies to the divine essence and attributes.
Difference in meaning only says that the conceptual contents of two terms are not fully interchangeable. It does not by itself establish independent existence for each.
A relational term therefore cannot be made to yield a conclusion absent from its definition. The discussion requires separately identifying meaning, existence, and relation.