Would you really expect a pediatrician to engage in open discussion about the same topic with every meshugener anti-vax parent who comes in? She’s come to her conclusion a long time ago, and has every right to say that if you don’t agree with her approach, go find another pediatrician.
A lot of pediatricians are overbooked as it is, and some don’t take new patients at all. Why should they waste their time rehashing the same nonsense over and over again?