The term narcissism originates from Greek mythology, where the young Narcissus fell in love with his own image reflected in a pool of water. While this is about how a natural person may behave it can certainly also be applied to how a company behaves.
Not to show empathy to customers
I think we all know the classic sales presentation with endless slides about how big and wonderful the selling company is and how fantastic the products they sell are. This approach contradicts everything we know about selling, which is to start with the needs and pain points at the buying company and then how the selling company effectively can fulfill the needs and make the pain points go away.
Not to show empathy to trading partners
While business outcomes originate from selling to your customers it certainly also is affected by how you treat your trading partners and how you can put yourself in their place.
An example close to me is exchange of product information (product data syndication) between trading partners. We often see solutions which is made to make it easy for you but then being difficult for your trading partner. This includes requiring your spreadsheet format to filled out by your trading partner, may be a customer data portal set up by a manufacturer or opposite a supplier data portal set up by a merchant. These are narcissistic dead ends as told in the post The Death Trap in Product Information Management: Your Customer/Supplier Portal.
The emphatic way forward is putting your company as being an active delegate in a business ecosystem as examined in post A Product Information Management (PIM) Solar System.