Relating to the word "Pusillanimous", it means to lack courage or resolution. When someone "pussies out" it means they have no backbone, or lack the courage to do something.
"Hey man, you should come chill with us later and take some ecstasy!"
"Sorry, but I don't want to lose an ice cream scoop of my brain cells, thank you very much."
"C'mon man, don't pussy out on me."