Inviting team members to your org is a great way to get your coworkers up and running on CircleCI. Why does a team member sometimes not show up on the list?
The primary reason is that they already have a CircleCI account. The invite members drop-down will only show people who don't have an account already, so it's possible your missing team member is already using CircleCI for building and testing their own projects.
If you send them a direct link to one of your organization's projects on CircleCI, such as a build URL, they can follow the project, and they will then show up in your team listing.