Well, in my place it’s not unusual to write a return address: you can buy postcards with pre-printed lines and boxes for address and zip codes. So on the down right corner it’s marked as address of recipient “To whom”, and on the up left corner it’s marked “From who”.
Sometimes “From who” and “to who” lines are printed on the same left side of the postcard and in that case it might be confusing.
As @ Florallle noted, if you placed your return address on the card, that may be why it got returned. For that reason, if you must put your return address on a card, put it in a VERITCAL position on the card. If you placed it horizontally, the automated system cannot distinguish who is the sender and who is the reciptent.
Did you write the address in foreign signs like chinese? Than that may be the reason. As far as I know USPS requres the address to be written in latin letters
It may say that officially, but as long as the country is written in English they send it there. Mine have always been delivered.
This happened to me once. The sender wrote their adress veeeery small just below my adress and USPS sent it back to him. It can always happen that the sorting machine reads the wrong adress as the receiver‘s adress. Put your adress in the left upper corner or don‘t write it at all then this shouldn’t happen again. 
If I remember correctly, other American Postcrossers reported earlier, that they also got their cards returned for the sorting machine obviously identified the return address as destination.
I think if it’s wrongly delivered/returned without a reason, there is no need to pay the postage again.
I would take it to post office or kiosk, and explain, and maybe remove my address label.
The same thing has happened to me but I don’t have a my address on the postcard so I have no idea how it even got sent back to me in the first place!