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All atoms are more stable when their outer most electron shell (valance shell also refered to as a valance orbital but it is slightly different) is full of electrons. Non metals generally have almost full valance shells and it takes less energy to gain a few electrons to reach the stable full outer shell than to lose many electrons to form a stable full outer shell.

Take F as an example - it has 7 electrosn in its outermost shell and this shell can fit 8. It will accept 1 electron more easily than losing 7.

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