Statement 1: Carbon always forms covalent bond with other elements.
Statement 2: C+4 and C−4 ions are highly unstable.
Statement 1 and statement 2 are correct, but statement 2 is not the reason for statement 1.
C−4 and C+4 are unstable,
C−4 is unstable because it would be difficult for the nucleus with six protons to hold on to ten electrons, that is four extra electrons than it is used to.
C+4 is unstable because it would require a large amount of energy to remove four electrons leaving behind a carbon cation with six protons in its nucleus holding onto just two electrons.
Carbon overcomes this problem by sharing its valence electrons with other atoms of carbon or with atoms of other elements. The shared electrons revolve around nuclei of both the atoms. Not just carbon, but many other elements form molecules by sharing electrons in this manner.