When you consider any new piece of software that's in the market. User Experience isn't necessarily a thing normal people talk about. Its usually commented for having 'nice looking' UI, if at all. However, the key difference of having exceptional User Experience vs having minor/or not at all is simply the retention of your end-users.
Now I myself am a software engineer, So I get my fair share of exposure to the importance of User Experience on a daily basis. Having worked with several open-minded clients, clients that understand there is a problem as well as clients that just want a software or an application for a particular requirement, I have understood that some of them have a bad reaction when an engineering team take time to improve or define an exceptional UX into an application.
Now, why is it important to sell it?
Why isn't it a given in today's day and age?
The answer is simple. Most clients that you work with understand it but the actual decision-makers of the project aren't actually that understanding. But, before we answer how to sell the importance of UX to archaic clients we need to understand the varying form of UX that appear in a project.
For Example, User Experience for the end-user mainly relies on how easy, intuitive and effective a particular piece of software is. The software could look amazing and everything could be in the exact place you need it but if a particular action takes ages to respond then the end-user retention is lost. Much like this example, UX can be inculcated in every step of building a software in order to create an experience/service and to make our end-users, as well as our Clients, lives a lot smoother in the long run.
Now on to the actual solution, If you have a client that is being a bit unresponsive or frustrated by the efforts that you put in UX in your application, there is one simple solution. Most of these archaic clients are much more familiar with numbers, so the easiest way to show is by showing the progression and long term value of your efforts. If you can show the percentage of end-users that can be retained with the right use of prediction and the financial or other gains, I guarantee you that it would be a lot easier to sell the importance of User Experience.
P.S: don't forget to show them the difference between UI and UX, some of them aren't aware.
Thank you.