Either-
Stop worrying about it and let him keep it as long as teeth are brushed after milk before bed. There's no teenagers running about with bottles, he'll give it up eventually anyway.
Or,
Put water in the bottle and deal with a couple of days of screaming. It won't be the last time you have to make a parenting choice that's for his own good that makes him unhappy. That's not authoritative parenting. You can be firm and kind without being a tyrant. The sooner you get used to this the better or you risk going too far in the opposite direction to your parents and being a permissive parent, which is just as damaging.