"une chaussure" is feminine.
All determiners have to agree with the noun they modify:
- une chaussure, la chaussure, ma/ta/sa chaussure, cette chaussure
Either "his" or "her", because in French, possessive adjectives do not agree with the owner but with the thing owned.
My instructor taught that "son" is for male and "sa" is used for female objects. But in Duo is completely different. So, which is actually correct?
Your instructor was right: "son" is for a masculine object, "sa" for a feminine object and "ses" for plural objects: "son frère, sa chaussure, ses amis".
In addition, "son, sa, ses" are used for both masculine or feminine owners.
Therefore "sa chaussure" can translate to "his OR her OR its shoe"