You can only change a person's mind if they feel that you are on their side, that you are not the enemy. The key here is to put yourself in his place and not be in a hurry.
Start taking an interest in his idea. Ask him about it, how he came to that conclusion, what his sources are. Make him see that if you were in his place, you would think the same.
Once trust has been established, try to find a point on which you both agree.
From there, with questions, take him step by step to the evidence. You can show him facts, but little by little.
The process has to be done in such a way that he discovers the reality himself.
You can't convince anyone. You have to help them convince themselves.
Following this process, a pediatrician from Madrid, Dr. Roi Piñeiro, managed to vaccinate 90% of the children whose parents refused to vaccinate them.