This is very strange.. You should have gotten a male and a female pet of the same species from the tutorial.. Did you use any items on the pets that wasn't in the tutorial?
I'm not sure at which point in the tutorial you are and if you have access to the pound yet, but if you do, I'd say to go to the Pound (Pets -> Pound) and just adopt a pet of the opposite sex.. If I remember correctly, at one point you need to adopt a pet from the pound, so should you have done that already, you may have to wait for the next day before you can adopt another.
Otherwise I would suggest contacting Support (Contact Us link at the very bottom) and see if they can help you.
Oh yes, the Breed button is on the pet profile on the right side, underneath "Gift Pet", "Private Sale" and "Sell on Auction" (if those buttons are the same during the tutorial). Make sure you have your female as active pet, click the button and then select your male pet from the menu that follows.