When we display emotions, we are in some sense displaying vulnerability. When we are displaying vulnerability, we give others opportunity to hurt and embarrass us. Yet, at the same time, if you we do not give others such opportunities, then we cannot know if we can trust them. Without emotional communication, there would be no purpose for friendship or relationship because there is no trust.
If you find yourself emotionless with some people, than that is fine because you simply do not trust them.
If you find yourself emotionless to everyone, than that is not fine because you have a fear of showing vulnerability. Without vulnerability, there cannot be any form of genuine relationship.
At the same time, when someone reveals to you their vulnerabilities, it is your time to show you can be trusted by supporting him/her forming a closer friendship and relationship.
For anyone to feel close to you, you also need to reveal some form of vulnerability. We are all human. We all have flaws. If one person reveals a flaw, it is best you reveal yours so he/she does not feel so left out.