I mean, how would you feel if you were a loyal secretary for a "Dr Smith"
for 20 years, and he hires a new secretary straight out of High School with no background and no experience, and pays her the same wage as he does you? Now would that be "fair"? I think not.

The problem with the "income ine******y" argument is that it does not reward workers based on merit. Everyone is paid exactly the same, and that is simply "not fair." It sounds "fair", but its not.
I have been working the same job for 13 years. I do not want to be promoted because I have young children. But why should someone who has recently gotten the "same" job as me, be paid the same as I have when I have been a loyal employee to that same position for 12 years?
See, the "income ine******y" argument leaves no room for job longevity, job experience, training, background, or education. If everyone receives the same pay for the same job, where is the motivation for the employee to gain an education, better their training, stick to the same job for several years, or take business risks?