Maybe your chat is disabled
Why can't I chat with other players?

I don't understand his account is 6 months old approximatley, so you should definitley be able to chat.
Like someone else said earlier perhaps your messages is disabled, if this is the case:
1. Go to your dropbox on the left hand corner and hover over your profile
2.Click on settings, or tap on settings
3.Go to messages/chat and turn it on if it is disabled.
If it is not disabled still go to your settings to see if you might have turned it off and forgotten or something along these lines...
If this doesn't work I would ask another friend for some help that may know what this issue is, and if they don't know I would then go to ask a chess.com reprsentative of your situation.
I don't know.