Why doesn't the STM32f0 go to the interrupt routine? (in the debugger)
You should be able to put a breakpoint at the start of the ISR. 
Then let the program run as normal without any stepping.

When you click the button, it should stop in the ISR and be in the debugger.

I would expect when the program is 'stopped' waiting for an interrupt, either the debugger allows interrupts to happen at full speed, and you won't see them in the debugger unless they contain a breakpoint, or the debugger is blocking interrupts.

If that is not the case, write back to say what is happening.