In JIRA, you can create quick filters so you can easily find your issues based on some custom filterings. For example, I have the following quick filters:
When I click each one of them I want all others be become deselected. How can I do this? Right now they all stay selected when I click around.
The answer is: you can't. They are just designed as a toggle buttons.
But... if you are really depressed to do that you can create JIRA plugin which will inject some JavaScript to do that for you ;)