Addition of oxygen and hydrogen can be useful to predict oxidation and reduction in most of the cases but this criteria fails to classify a reaction as oxidation or reduction when there are no oxygen or hydrogen atoms involved. This method is very primitive.
A better perspective :
Oxidation : Increase in oxidation state (by loss of electrons) of central atom.
Reduction : Decrease in oxidation state (by gain of electrons) of central atom.
If you already know how to find the oxidation state of the central atom (in your case carbon), then I hope you will be able to get your answer now.
The answer to the question why oxidation of alcohol to carboxylic acid takes 2 oxidation reactions, lies in the reaction mechanism. These mechanisms cannot be challenged, they are what they are. We can only observe and provide a acceptable explanation to why they happen like the way they do.