Confusions about oxidation and reduction
The formal definition of an oxidation/reduction is linked to the loss/gain of electrons. Considering the addition or loss of hydrogen and oxygen is not a global rule, but rather a trick generally used in organic chemistry. If you consider organic molecules, thus mainly composed of carbon, "adding" oxygen atoms suggests an oxidation of the carbon, as oxygen is more electronegative than carbon, while "adding" hydrogen atoms suggests a reduction, as hydrogen is less electronegative than carbon.

An example would be the successive oxidation of ethanol to ethanal, then acetic acid : $$\ce{CH3CH2OH -&gt;[-2 e^-][``-2\text{ H}"] CH3CHO -&gt;[-2e^-][``+1\text{ O}"] CH3COOH}$$