The phrase "to shut the door" means to close or block access to something or someone.
Sentences with «to shut the door»
When looking for your next opportunity, don't shut the door on jobs that you wouldn't necessarily apply for. (blog.simplyhired.com)
But at least he didn't shut the door on action. (madisonamps.org)
When the right person comes along, you'll know, and the most important thing is to not shut your door in the face of new opportunity. (loveprofileexpert.com)