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The sign does change in a reverse reaction. The reasoning is that since enthalpy is a state function, the energy required to push a forward reaction to its products would be directly reversed to push it back to its reactants.
You only need to change the sign because the destinations are reversed now. Point B goes back to point A as opposed to the forward reaction. This only causes a sign change because enthalpy is a state function and only depends on the state of the reaction and disregards the path.
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