No matter how much your entire organization sees a problem person or a behavioral issue, some people are just blind to their own flaws and their impact on other people. Frankly, with those people, you may just have to hit them on the head with a sledgehammer figuratively to wake them up.
Get Straight to It
If somebody cannot see their problematic behavior no matter how many times you try to lead them to it, your only option is to be brutally honest about it. Tell that person exactly what the problem is and exactly how their actions or words are hurting other people - or the organization as a whole. If the person can be coached counseled or trained in some way and they're willing to do that then that's your first step. But if they're not willing - or you realize that no amount of coaching can change this person - then well you just need to cut them loose. If you don't they'll drag the whole company down. A person who can't change through coaching or training of any kind is a person with a self-centered "it's all about me" attitude. That's not an attitude that's acceptable in any positive culture. Their behavior is detrimental to everyone and everything around them including people outside of the company like customers and vendors.
When to Cut Them Loose
Imagine an employee who is highly talented world-class in his (or her) field but has a work ethic that is not congruent with the rest of the organization - someone you know likely may have already come to mind. This person is lazy and no one can depend on him or her for anything. This behavior affects everyone else because when work isn't completed on time it results in a trickle-down effect - everyone who's relying on this output to complete their work is suddenly stalled. The whole system clogs up and the whole team or division is inefficient as a result. To make matters worse this individual leaves at 4 o'clock on the dot every day no matter what's on his plate. His teammates are working overtime and he's just walking away. You try to bring this to his attention but he just doesn't see it. So you pick up the sledgehammer to break down the walls and get brutally honest with him: setting an absolute deadline for his next project and tell him it has to get done or else. Guess what? It doesn't get done. Now you have no other option but to cut him loose: he's had every chance but he hasn't improved. If you don't let him go you'll lose the rest of your best employees. They'll get so frustrated with this guy that they'll bring their time and talent elsewhere. Do what you can to help your employees improve - even if they're as blind as a bat to their shortcomings. If they don't respond to the sledgehammer then they don't belong at your company.