The ongoing debate is whether getting the general public to wear masks is actually helpful or not.
See my other response for ways in which that differs from medical staff doing it. It's psychology and sociology as well as pure "can a mask stop the virus", which are important factors when looking at disease transmission in a population.
Healthcare workers wear masks of a known quality, which they have fit tested, and they know how long to use them and when to dispose of them. They wear them as part of a full protective strategy along with other context-appropriate equipment and have training to know how to conduct themselves in the situation too.
You can't just claim the same benefits for an old piece of t-shirt stretched across your face. An old piece of t-shirt which may give you a false sense of security and lead you to take risks and get closer to other people, and which may make you touch your face more, and which you may not clean or replace etc etc...