Can a 12 year old have the right to refuse to see his father on father's visitation day?

Legally, the child cannot refuse and must abide by court orders.  Whether law enforcement would enforce it, that is another question.  When children are older, law enforcement becomes less interested in forcing visitation.  If you are the one wanting the visitation, I would check with the local authorities to see if they would enforce it.  Before that, I would think about the primary question: whether it is a good idea to insist on visitation if the child resists.