Why do nonmetals have both positive and negative oxidation numbers?

The chemical elements can be broadly divided into metals and nonmetals according to their tendency to loose or gain electrons:

• Atoms that belong to metallic elements tend to loose electrons. When they loose electrons, they become cations, positive ions with a charge that equals the number of electrons they have lost. That number is given by the oxidation number. For instance, sodium's oxidation number is +1, while calcium's oxidation number is +2.
• On the other hand, atoms that belong to nonmetallic elements tend to gain electrons, so they become anions, ions with a negative charge that equals the number of electrons they have gain. For instance, fluorine tends to gain one electron and becomes F^-. That is why it has oxidation number -1. 

But, as we can see in the following periodic table, most nonmetals have both positive and negative oxidation number:

Why do nonmetals have both positive and negative oxidation number if they always tend to gain electrons?

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers.