CHEMISTRY COMMUNITY

When we flip a reaction, for example flipping Ni2+ +2e- --> Ni to Ni --> Ni2+ +2e- to show oxidation, why don't we flip the sign of the reduction half potential?

Keep in mind "standard reduction potential" specifically refers to the reduction form of the half-reaction expression, always. If you write the half-reaction as an oxidation, then yes, you technically do flip the sign, but you must not flip the sign if you are going to use the formula E°_cell = E°_cathode - E°_anode. This formula is only true if standard reduction potentials are used.