Nannyde is right, I can't/won't allow cups from home either.
It is horrible and disruptive since the kids target each other for the "cool" cup. It triggers more fights than toys from home since the "reward" is instant if a child manages to get the other child into submission.
The center is trying to protect your child, they see these patterns all day long.
I was also thinking they may be referring to cleansing/sanitation rules and regs. If they cannot guarantee the proper cleansing classroom teachers may view it as "illegal" to take them in. YKWIM?