Chemistry - Why do atoms "want" to have a full outer shell?

Solution 1:

You are attaching too much importance to Lewis structures. The 8-electron rule and Lewis structures which are derived from it are only rough guidelines for working out the electronic structure of a compound in very broad strokes. Often these broad strokes are accurate enough to make some meaningful statements about molecular properties but it does not accurately describe the true electron or charge distribution in a compound. Take water for example. As you say, the 8-electron rule would predict that the hydrogen atoms each transfer one electron to the oxygen molecule which would then carry a charge of -2. But experiments show a different result: here you can find a paper that determined

that a charge of approximately $0.5 e$ is transferred from each hydrogen atom to the oxygen

which would amount to a partial charge of $-1 e$ on oxygen and here you can find a similar claim:

The charge distribution depends significantly on the atomic geometry and the method for its calculation but is likely to be about $-0.7e$ on the O-atom (with the equal but opposite positive charge equally divided between the H-atoms) for the isolated molecule.

And there not being a $-2e$ charge on oxygen is quite understandable if you look at the electron affinities of oxygen (e.g. here): You see that the first electron affinity is $-142 \, \mathrm{kJ}/\mathrm{mol}^{-1}$ and thus energy is gained by the process of transferring a free electron to a neutral oxygen atom. But the second electron affinity is $+844 \, \mathrm{kJ}/\mathrm{mol}^{-1}$, so another electron transfer is very costly. The quite extreme situation of a -2-charged oxygen described by the 8-electron rule is very rarely found in real compounds. Even in ionic compounds like $\ce{NaCl}$ the electron is not 100% completely transfered from the electropositive to the electronegative element.

Solution 2:

Its not a problem about being charged, its about the symmetry. The quantum states of those valence orbitals are stable, in that there is little interaction with the other electrons. Since there are already filled orbitals, electrons will want to bind to complete the shell because as it happens extra binding energy is available. With a full shell maximum binding occurs.