But maybe Visa and Mastercard don't want to deals with bitcoins?
Yes, for two reasons:
1.) They don't want you to speculate using their money.
This is the same reason you cannot add money to an E-Trade account using Visa and Mastercard either.
2.) Bitcoin is not only a formidable competitor to them, it is is more likely something that will be eating a good chunk of their business. The longer they can avoid competing with Bitcoin the better.
That being said, it is doubtful Square will know for what reason you swiped a credit card through your friend's iphone, for instance. So they likely aren't stopping it from happening entirely but they are keeping using credit that way to a manageable level.