There's an option in account privacy settings to alter who can start a conversation with you. It can be all site members (the default), only people you follow, or nobody at all. The person you are trying to contact may have changed this from the default setting.
I think this also might happen if the person has you blocked, but I'm not 100% sure of that.
You'll have to try to contact them some other way to figure out what's going on there.