Badass kitten goes into attack mode every time rescuer tries to set it free

Size appears to be irrelevant, since cougars purr but are not small. It depends on whether or not they have hyoid bones that can vibrate or not. Non-purring cats have flexible hyoid bones, enabling roaring, purring cats have solid hyoids that can vibrate but cannot bend into a roaring configuration.

(The second link has footage of a purring cougar, among other cute bits).