Oxidation and reduction always must occur at the same time! You cannot oxidize something without reducing whatever is doing the oxidizing. The reason for this is based in how oxidation-reduction (redox) reactions work.
When you go through a redox reaction, you are effectively removing the electrons from one substrate and transferring them to another. A key point here is that electrons do not tend very often to be on their own! There are some exceptions to this, such as beta particles and conduction of electricity through metal. However, in terms of chemical reactions, electrons are always coupled to atoms or molecules.
A great example here is to look at batteries. The traditional galvanic cell involves copper and zinc, where electrons are transfered from zinc to copper. Here, the zinc becomes oxidized, as it loses electrons. At the same time, copper is being reduced, as it is gaining electrons. If there were no receptor for electrons as the zinc is oxidized, the oxidation would not proceed! Similarly, the electrons that come in to reduce copper are not created out of thin air.
I hope that helps!