> I've literally never had the thought of "how do I influence other people." Why is that considered a valuable skill?

If you're a software developer you must have thought "current priorities are not right, we should do X for the users / Y to get better quality" and tried to influence your management to get those priorities moved. Maybe by starting a campaign with your users so the demands come from multiple services and not just you, or by measuring quality indicators and showing how what you want to implement would improve them etc.

That's why you want to start getting coffee with people, maybe go outside with the smokers. It can take months of "work" to get people to propose the idea you want done.

But this kind of influencing won't help your career.