When you are looking for synonyms for the phrase "closed door on," there are a few phrases that come to mind. Some possible synonyms include "shutting out," "denying access," "blocking entry," "refusing to engage," and "shutting down." All of these phrases capture the idea of closing off or rejecting a possibility. This could refer to anything from ending a relationship or a job opportunity to refusing to consider a new idea or approach. Whatever the context, the common thread is a sense of exclusion or rejection, of shutting the door on something that might have once been open.