Why does it make sense that if an atom loses electrons, it is left with a pisitive charage?

Because atoms are neutral. By neutral, I mean that; there are three main particles that make up an atom. Protons, Electrons and Neutrons. Protons have (electrically) positive charge, electrons have negative and neutrons are electrically neutral. One proton's charge is +1 and one electron's charge is -1. An atom (normally) has the same amount of protons and electrons. Let's say if an atom has two protons and two electrons, the sum of electrical charges of the protons is (two times +1) +2 and sum of electrical charge of electrons is (two times -1) -2 . The total charge of the atom is the sum these. So, (-2)+(2)= 0. That makes the charge of the atom 0, thus makes it neutral. But let's say this atom loses one of its electrons, and now has only one. So one electron (-1) and two protons (+2) in total will be : (-1)+(2) = +1 . +1 is positive, so this makes the charge of the atom positive.

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Nonmetals usually react by gaining electrons