What people do for a living takes up about half of their waking life (and they probably dream about it too), so it will tell you so much about the person. Personally I love my job and what I do, so I really want to talk about matters at least related to it because my life does revolve around it indeed. So establishing some common ground with the other person can really help to start the conversation.
But of course the conversation doesn't have to specifically be about either job through progression.
But only if you know the person well enough to have the context of it. What a person's job says about them is very different, for example, if they love their job vs hating their job.
Love or hate the job, knowing what it is gives you insights/guesses into skillsets, education level, economic level, possibly the type of people they mingle with, etc, etc.
But of course the conversation doesn't have to specifically be about either job through progression.