First, let me just say that this has not happened to me, and therefore I only know from troubleshooting other issues with people, but this is the most common answer.
What you're going to need to do, is access your YouTube account by signing in, of course.
Next, you will want to go to "account privacy". This will take you to your YouTube Privacy settings. (If not, log in first.)
Then, just look over your selected options. The issue may be apparent just by reviewing your settings, but if you can't figure it out still, be sure to make sure, first and foremost, that the box labelled Make Comments Private (or something of an equivalent meaning) is not checked.
For future reference, please make sure to check all of your settings regardless of what you may think they are set to. There is an extremely high chance that it is something as simple as one or two check boxes!