they get more and more electrons, which are weaker and weaker bound, thus form metals

I mean… What kind of answer are you expecting? We can’t know why the universe is how it is, we can just observe that it is like that.

I mean why is the speed of light that specific value and not faster or slower? It just… is.

Your question is more philosophical than physical.

Metals have what’re called delocalized electrons, where electrons just kind of wander around a metallic bond between atoms. Metallic bonds involve a very low level of attraction between the nucleus and its electron cloud. Turns out most elements have this, so they do metallic bonding.

It’s only when atoms start to get a little wobbly do they exhibit enough electronegativity to perform ionic or covalent bonding, where the molecules donate electrons. Electronegativity increases on the right side of the periodic table when electron valency starts getting lower. And that’s the non-metal side.

So the answer is basically that you need more of an electrical charge to exhibit the things we’ve classified as non-metals. Metals are more chill and generally less reactive.

I should also mention that non-metals have a liquid/solid metallic phase at certain temperatures and pressures. I remember a Chinese study a few years ago claiming to have made metallic nitrogen.

I think that we have a perception bias towards things that interest us.

Since the elements in the top-right corner (C, O, N, P, S, Si, Fe, Al, Na, …) are interesting to us, that’s what we typically look at. And in that region, things are fairly balanced. It’s only in the regions where we don’t typically look, where we said “let’s just make it all metal so the categorization is done, call it a day, and move on”. I think.