At the end, there cannot be a man and a woman both unengaged, as he must have proposed to her at some point (since a man will eventually propose to everyone, if necessary) and, being proposed to, she would necessarily be engaged (to someone) thereafter.
Let Alice and Bob both be engaged, but not to each other.
Giving one group their first choices ensures that the matches are stable because they would be unhappy with any other proposed match.
The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of rankable applicants for a position.
The applicants are interviewed one by one in random order.
Billions of users access web pages, videos, and other services on the Internet, requiring each user to be matched to one of (potentially) hundreds of thousands of servers around the world that offer that service.
A user prefers servers that are proximal enough to provide a faster response time for the requested service, resulting in a (partial) preferential ordering of the servers for each user.