I’m afraid that checkboxes aren’t actually an input option for the ticket selector. If they’re radio buttons that means you probably set the “Maximum number of tickets allowed per order for this event:” option to 1. That will actually limit the total number of tickets for the event to 1.
It sounds like you want the quantity per ticket to 1, and that can be set in the Advanced ticket options section (you click on the gear icon to open the Advanced options). You’ll set the Maximum Quantity field there to 1.