I think a dirt bike is safer than an atv Jen.
Because it is harder to exceed your limits when riding a dirt bike but on an atv you "feel" safer so you tend to get in trouble faster.
Also, dirt bikes are lighter so when you do get in trouble ... chances are you can save it!
Talk to your dad, he sounds like he is very concerned about your safety ... But if you show him a web-page for the MSF dirtbike school
http://www.dirtbikeschool.com/ and explain to him you want to learn to ride because it is important to you but you want to do it responsibly ... he will cave in and set you up!!!
Good Luck