A reaction in which electrons are transferred between two reactants participating in it can be termed as redox reaction.
Here gets oxidized by losing two electrons and gets reduced by gaining two electrons, hence oxidation number of the reactants changes.
In case of acid-base reactions, there is a transfer of hydrogen ions instead of electrons, and the transfer of hydrogen ions does not change the oxidation number
Here the oxidation number of the elements remains the same.
Hence the acid-base reactions are not redox reactions.