Why isn't hydration an oxidation reaction?
As context is always King, I will briefly mention that the original quote is about the redox chain from carboxylic acid via an aldehyde to a primary alcohol (and potentially to an alkane). In this context, the aldehyde is capable of adding water as shown in $(1)$, but this reaction does not constitute a redox process in any definition of the word (count electrons).

$$\ce{R-CH(=O) + H2O &lt;=&gt; R-CH(-OH)(-OH)}\tag{1}$$

In other cases, the removal or addition of water does change the oxidation states of various carbon atoms as you observed. This is not only true for the dehydration of an alcohol as in your example but e.g. also in such key reactions as the Wittig reaction or the Suzuki cross-coupling.

However, organic chemistry deals with a great number of individual synthetically useful reactions that must be classified in some way or another for humans’ benefit. In this organic chemistry classification system, only those reactions that


unilaterally oxidise a single carbon atom by means of addition of an oxygen atom or removal of hydrogen atoms; or
concurrently oxidise two carbon atoms bound to each other by the addition of oxygen or removal of hydrogen in such a manner that both oxidation states change by the same value


as oxidations. (And vice-versa for reductions. Individual exceptions most certainly will apply.) Your example is, in inorganic terms, a comproportionation which means one carbon is oxidised while the other is reduced. Not only does this not cleanly fit into ‘carbon is oxidised’ or ‘carbon is reduced’, meaning it creates a terminological mess, but it also would subsume most if not all reactions under the general redox labels which destroys the idea of classifying reactions as oxidations or reductions in organic chemistry altogether.

So: yes, in a strict (inorganic) sense it is a redox reaction, but in the interest of a more practical classification of organic reactions it is not considered one.