VBACs DO still occur often and successfully. There are some specific things that have to happen for a VBAC to be considered safe. First, you have to have had a low-abdominal transverse incision, (not a vertical midline incision) with your last C-section. The transverse incision looks like this --------- across your lower abdomen. With a midline vertical incision, there is more risk of VBACs splitting the uterus during labor.
Second, you should have at least 24 months between your C-section and your next delivery, to allow time for the surgical sites to fully heal before attempting the stress of another labor.
Those are the biggest factors, but there may be more, specific to you.
Any MD that tells you that VBACs aren't done anymore is just not teling you the truth. They are done, in fact, they are done more often and more successfully all the time. It sounds like he just doesn't want to do them himself. If you want to consider a VBAC, you might have to find another MD.