Plenty of testers claim that they break the software. They don’t really do that, of course. Software doesn’t break; it simply does what it has been designed and coded to do, for better or for worse. Testers investigate systems, looking at what the system does; discovering and reporting on where and how the software is broken; identifying when the system will fail under load or stress.
It might be a good idea to consider the psychological and public relations problems associated with claiming that you break the software. Programmers and managers might subconsciously harbour the idea that the software was fine until the testers broke it. The product would have shipped on time, except the testers broke it. Normal customers wouldn’t have problems with the software; it’s just that the testers broke it. There are no systemic problems in the project that lead to problems in the product; nuh-uh, the testers broke it.
As an alternative, you could simply say that you investigate the software and report on what it actually does—instead of what people hope or wish that it does. Or as my colleague James Bach puts it, “We don’t break the software. We break illusions about the software.”