Why do nonmetals form anions?

Non-metals typically have a high charge/size ratio, which causes them to attract electrons. They typically attempt to reach their objective of a noble gas configuration by either gaining or losing electrons. Since non-metals have a high charge/size ratio, removing one or two electrons is easy, but removing all of them requires superhuman strength, or extremely high energy. The same is true for non-metals; if you want to remove all of the electrons, you need an extremely huge amount of energy, which is not possible thermodynamically. If they gain electrons, you can easily reach a noble gas configuration.

As a result of their tendency to gain electrons in order to reach a stable electron configuration—usually by filling their valence shell—nonmetals can form negatively charged ions (anions) when they achieve a full outer electron shell, which is more energetically favorable.