Answer
Oxidizing agents are called this way because they oxidize the other element. Therefore, they are reduced and they oxidize the others. In other words, they are the elements that gain electrons.
Reducing agents, on the other hand, are oxidized (lose electrons), and thus they cause other elements to be reduced.
Work Step by Step
Oxidizing agents are reduced (gain electrons).
$cu^{2+} (aq) + 2e-$ --> $ Cu (s)$ (reduction reaction)
Copper ions are the oxidizing agents.
$Zn (s) $ --> $Zn^{2+} + 2e-$ (oxidation reaction)
Zinc here is the reducing agent as they caused copper to be reduced.