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LingakuLingaku与其说 + [A]，毋宁说 + [B]
与其 + [verb phrase]，毋宁 + [verb phrase]
[clause]，毋宁说 + [clause]
毋宁 means "rather" in the second half of a comparison. With 说 it corrects a description: "not so much A as B". Without 说 it chooses the better of two actions. It is the literary version of 不如, and it nearly always follows a 与其 clause.
The first label isn't wrong, only less accurate, and the sentence lands on B.
与其说…不如说… means the same in plainer writing and has its own point.
Without 说, the pattern weighs two actions and prefers the second. Ordinary prose uses 不如 or 宁可 here.
毋宁说 can also follow a clause that has just rejected a label.
与其 carries the label being set aside and comes first. 毋宁 carries the one the writer stands by.