The reason that can be given for the incorrectness of the second sentence is as follows: both if -clause and unless -clause in your example are conditional; the unless -clause is roughly synonymous with a negative if- clause, but UNLESS PLACES GREATER EMPHASIS ON THE CONDITIONS AS AN EXCEPTION ('ONLY IF... NOT'). Therefore, in some contexts unless- clauses are impossible.
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AnonymousGrammar books say a sentence like "She will be angry if I do not visit" is correct but a sentence like "She will be angry unless I visit" is incorrect. Why?I don't see anything grammatically wrong about "She will be angry unless I visit". I think the point is that the two sentences do not have the same meaning, not that one or the other