usage - Are 'third person singular pronouns' optional?

Generally, two occurrences of the same name aren't used this close to one another. Consider the following two sentences:

• John went home. John turned on the TV.

This sounds marked to most speakers. (NOTE: markedness is not the same as ungrammaticality). The reason it sounds marked is because there are collocation restrictions on names.

These restrictions occur because of a general rule, as Kent Bach notes:

"We generally choose the least informative sort of expression whose
use will enable the hearer to identify the individual we wish to refer
to" (see p. 9 of this)

Pronouns are less informative than names. So if a name has just been used, we usually use the pronoun, since the fact that the name has just been used gives us enough information to figure out the referent of the pronoun.

Your teacher seems to be confusing the markedness of your response with its ungrammaticality. If it's a class which is trying to teach you how to be conversationally fluent, she might be justified in giving you partial credit, but I'm not sure.