It does not mean that everyone has an equal chance at success. You have no control over the experience your students bring to class. You have little control over the resources outside class that they have access to. It is not worth your time to try to level out every little bump in the playing field even though each bump seems like a mountain to at least one student. The sooner students learn to use their strengths and to recognize and work around their weaknesses, the better off they will be.
Students are responsible for arranging their lives around their priorities.
If a student needs a certain grade in your class to change majors, stay in school, get a job, win a scholarship, inherit a fortune, etc. Students who are painted into corners have done so themselves. At worst, you will be the last straw but you did not put all the straws on the camel's back and you did not choose the camel. Students are responsible for managing their time. If a student is working two part-time jobs, taking 18 credit hours, helping out at the soup kitchen and failing your class, he or she is still failing your class.