I am not opposed to humans drinking cow's milk...but 40 ounces is WAY too much...I think you realize that.
He is definitely old enough to master this. I wouldn't necessarily take the bottles away cold-turkey, but I wouldn't give him milk in them anymore. If he wants milk, he can have it in the cup.
Some kids need the comfort of suckling longer than others. I introduced the cup around 6 months. Bottles were gone before her first birthday. BUT I nursed her until 18 months AND then she wanted her pacifier back after weaning for napping and sleeping at home. Interesting enough, she never used the pacifier after 8-9 months at the daycare...go figure.
Unless there are some other issues at play, he'll eat when he gets hungry enough. This is a huge time of testing limits. I am pretty relaxed about what my daughter eats. We keep healthy, acceptable choices in the house and she can have some choice in what to eat (I don't COOK multiple meals). If she doesn't want what is for dinner, she can have a bowl of cereal or a peanut butter sandwich. Most kids can understand and master this choice at two. She has gone to bed without dinner 3-4 times in the last year (she is three now) because there was some sort of meltdown at dinner.
Laurie and I agree on most things...lol...but some daycares/preschools DO require sippy cups. It is actually one of things I don't really like about mine. I don't think they are really helping the kids by not helping them master an open cup in every day situations.