There are lot of reasons for not using Facebook to log-in to websites and apps - it doesn't make you a Luddite or part of The Anti-Social Network.
For many people, Facebook is a private and not a public thing, used to interact with real-life friends, not the world at large. Others are simply uncomfortable about giving access to their Facebook account willy nilly. People get suspicious that what they do on the site or with the app will start appearing on their timeline. Still other people are uneasy about handing yet more of their personal information and photos over to Facebook, not knowing how it might be used in the future.
For these reasons, one of the most common complaints by users is when a service requires users to sign-up and log-in using Facebook. The issue is so prevalent that even Facebook themselves made it so you don't need to have a Facebook account to use their Messenger app. Even Facebook accepts that not everyone wants an account on its social network. Yet many services still require Facebook accounts while others are owned by the social networking giant, making all your posted content, including your photos, fair game for whatever intentions Facebook may have in the future.
never asks for your Facebook username. You do not need a Facebook account to sign-up and use the service. All you need is a username and email address (which is never shown to anyone and never spammed). Share and interact with your your contacts whether or not they’ve joined Facebook.