From that wiki:

> Private set intersection is a secure multiparty computation cryptographic technique[1] that allows two parties holding sets to compare encrypted versions of these sets in order to compute the intersection. In this scenario, neither party reveals anything to the counterparty except for the elements in the intersection.

Revealing even elements in the intersection, if that means revealing individual votes, breaks ballot secrecy.

Exactly, it means someone you could prove to someone else how you voted, which is the sine qua non condition for creating a vote economy. That's actually the main reason behind trying to keep the vote secret, much more than threats of intimidation for opposing parties voters, etc...