I figured out what’s causing this issue on my blog. I’m using “Category Levels” plug-in. Therefore, some of the categories are Private and accessible only with login. The problem is that by default I have new posts go to a Private category. I had no idea that it also affecting Pages. The only way I figured it out is by looking at MySQL table: wp_post2cat. I manually changed Category ID to Public category and the pages showed up on the blog.
Anyone knows if there is a way to have Pages be created in a complitely separate category because once the Page is created I see no one of changing Category through Control Panel.