I've come to believe that understanding what empathy is and how to develop it is easily one of the most important skills we have in all stages of life, and the lack of it is one of the most common reefs that people crash on in adulthood.
You really see the effects in the tech industry, as many of us were drawn to this line of work when we were undersocialized introverts in our teens and 20's. I know I was. I really resented social pressure in all forms, and was always pissed off that everyone else didn't see me for the genius that I thought I was at that age (which I was not, of course, but that belief was the only thing that got me out of bed some mornings). I loved the idea of a job where all that mattered were my technical skills, and never had to interact with other people, not realizing that any engineering job worth having would not fall into this category, if such jobs even existed.
I frequently see people get angry in forums when they think people are arguing with them based on the tone or wording of what they said rather than the content of their post. I frequently see people make comments in forums along the lines of, "99.9% of humanity is just too freaking sensitive and I refuse to change myself to adapt to them." More topically, you will occasionally see politicians or other public figures brush off outrage against some mind-numbingly hateful or stupid remark with excuses like, "I don't have time for political correctness", as if their lack of PC-approved verbiage was the reason people got angry. All of these things are indicators of people who not only don't have empathy but don't even realize what it is. They think empathy is like sympathy, or some other warm and fuzzy lets-share-our-feelings thing that they don't think they need to understand.
But really empathy is just the ability to have at least a shred of intuition for how things look from other people's perspectives. I think of it more as a neurological function than anything else, another high level input that our brains synthesize for us from lots of low level activity that we're not aware of, not unlike sight or hearing. It's a prerequisite for effectively communicating things to other people, and it becomes even more important when the people you are communicating with are predisposed to disagree with whatever you're saying. It's not schmoozing, it's not knowing how to sugar-coat what you say so as to not offend people (although that's often a pleasant side-effect in touchy situations!), it has nothing to do with political correctness, it's not even a social skill- it's literally just having the tiniest sense of how you come across to other people so you can communicate as effectively as possible. It also makes it much, much easier to design software that actually solves problems for other people, and to arrive at the best possible compromises in personal and business dealings. It also will aid in your awareness of problems that might not matter to you, but matter a lot to the people whose problems you want to solve.