You cannot "disagree" with the formal definition of Inductive reasoning and Deductive reasoning ....
They are what they are.
From you link:
"Reasoning can run in two opposite directions. Deductive reasoning moves from a general premise to a more specific conclusion. Inductive reasoning moves from specific premises to a general conclusion. "
You are trying to construct a deductive argument based on a false premise.
The definition of Deduction and Induction are NOT as you believe ... No matter how much you believe it.
Moreover, confromted with the actual definition of Induction and Deduction, you are not accepting the new facts and readjusting your conclusion.
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