Math Easy Solutions, not quite — the anode does the opposite of “giving oxygen electrons.” At the anode, water is oxidized and loses electrons: 2H₂O → O₂ + 4H⁺ + 4e⁻ in acidic conditions, so those electrons leave the water and go into the anode/external circuit; at the cathode, electrons are delivered to water or H⁺ to make H₂ by reduction per Chem LibreTexts and Wikipedia. So oxygen in O₂ is neutral because it’s an elemental molecule, not because O²⁻ “gains 2 electrons” there — in fact the oxygen atoms in water go from oxidation state −2 in H₂O to 0 in O₂, meaning they’re being oxidized, not reduced. Your electrolysis thread is basically circling the key idea: the power supply pulls electrons from the anode side and pushes electrons into the cathode side.