Exothermic means energy is released during reaction. That is possible only when energy released in bond making products is higher than energy used in bond breaking reactions.
Negative sign is used for exothermic reaction and positive sign of ΔH indicates the exothermic reactions.
If energy released in making the bonds in products will be lower then reaction cannot be exothermic and it should be represented by positive sign which is possible only if we consider:
ΔH = energy used in bond breaking reactions − energy released in bond making products and not
energy released in bond making products > energy used in bond breaking reactions ; ΔH = - ve ; exothermic
energy used in bond breaking reactions > energy released in bond making products ; ΔH = + ve ; endothermic