A covalent bond is pictured as two electrons shared by two different atomic nuclei, which means that each of the two nuclei has two electrons. The problem I see with it is that it implies that if a hydrogen atom is neutral then a hydrogen nucleus in a covalent bond must be negatively charged since it has one more electron than a hydrogen atom. Which implies that a hydrogen molecule is negatively charged which is a contradiction (molecules are neutral).
Alternatively, one can say that the covalent bond is composed out of a single electron, which acts as a negative potential for both hydrogen nuclei hence it exerts negative potential of two in the molecule. But then the question is, where does the second electron go when two hydrogen atoms form a covalent bond?
My question does not relate only to this specific example, it's about covalent bonds in general.