There’s an amazing number of “but people are primates” comments. Correctness here includes specificity. If person and primate are both candidates, then primate isn’t a correct answer to what this is trying to do. You wouldn’t react to the phrase ‘treating women as objects’ by saying people are objects, right?
On the other hand, I think there's a semantic difference between your two cases. I'd argue that treating a woman as an "object" is a different sense of the word to how women (and men and teapots) are literally "objects".