Is it ok if I refuse to use a photo of myself as a profile picture on social media?
Whats wrong with having a photo of yourself on social media?
Because I want to hide behind a picture
If you dont want to post a photo of yourself on social media then you have the right to do this. You have a right to privacy, and nobody on the social media platform is going to force you to post anything that you do not want to post.
I should be able to not show my face online.
You are correct and I hope you don't listen to the peer pressure to show others what you don't want them to see on social media. You're in control of your privacy and if they don't like it, then they can find someone else to bother.