C, the major product is not the double bond rather it is the ether. Notice that one of the alcohol oxygens is left as a bridge between the two carbon chains connecting the carbons where the -OH groups were originally attached. Ethers can be produced by this reaction from molecules where a double bond is not possible, for instance, methanol which has only one carbon. There are two parts to the reaction, the reduction half and the oxidation half. In organic chemistry electron transfers may be hard to see, we therefore look for something simpler than counting electrons to identify redox reactions.
Oxidation occurs when the major reactant loses hydrogens or gains oxygen.
Reduction occurs when the major reactant gains hydrogens or loses oxygen. During the oxidation of alcohols, the molecule first loses a hydrogen and then secondly can gain another oxygen. To have an oxidation reaction, you need an oxidizing agent. Although your text shows the oxidizing agent as a catalyst, above and below the arrow, it is not really a catalyst. The alcohol is losing electrons, it is being oxidized, and the oxidizing agent is gaining electrons, it is being reduced.