It is completely normal that you see yourself being sympathetic by creating solutions, when people are asking you for empathy.
I'm writing a book aimed at developers on building empathy and applying it to business, called Deploying Empathy [1]. I'm writing it in public as a newsletter. I'm detailing specific actions you can take in conversations and customer interviews to build empathy.
One of the things about listening to people is that the more you do it, the more empathetic you become as a person. It takes practice, but I promise you will get there.
One of my own favorite books on this is Practical Empathy by Indi Young.
Self-empathy is also an important step, and if you find you don't have the tools to show empathy in conversations, there's a good chance this is a skill you weren't taught growing up. For that, therapy is invaluable.