This article is not terrible, but it is yet another article about listening that treats it as the direct exchange of information rather than as one dynamic in the embodiment of a relationship.
If you “talk about yourself” by sharing a similar problem, that is called commiseration. This can be a comforting move because it doesn’t put pressure on the other person to respond, yet implicitly expresses that you understand the feeling (assuming you are choosing a good example from your own life to share).
The particular technique of responding doesn’t matter as much as establishing the kind of relationship where either side can assert themselves as needed, and feels that the other side will let them. That way, the person who feels more need gets what they need.
My wife and I are coming up on our 35th anniversary. She’s very quiet and I am loud, so I have to force myself to leave a lot of space for her to assert herself (this has become easier over time, partly because I know that she will always give me what I need in the end, so suppressing myself never feels like a penalty).
I like the technique suggested in this post (draw her out by asking inviting questions about her situation). I only object to labeling the sharing of oneself as “egocentric.” In a loving relationship, your ego automatically serves your love-sworn. Offering of yourself can be exactly what she wants.
I am a listening trainer, and have taken over 1,500 people through a basic session in active listening. But that said, I agree with you that what matters is having a good relationship, and that involves using different communication skills at different times.