Kendall M. answered  07/17/19
AP Chemistry Teacher for 25+ years
I think I would approach this in a different way.
Nature is going to do whatever is easiest. Water flowing down a hill fill find the path of least resistance. Carbon easily forms covalent bonds, including double and triple bonds with itself. These bonds give off more energy, in other words are easier to make, than those that it can make with metals. Even when carbon does bond with a metal like lithium or sodium, it first makes a triple bond with itself with 2 extra elections called the acetylide anion, C22-, polyatomic ion. Then the acetylide will bond with 2 lithium (or 2 sodium) ions. Making Li2C2.