What are the advantages of a geared contrarotating turbofan?
what problems are stopping us from doing this?


In some sense, it's business reasons. Developing a brand new jet engine from scratch costs a lot of money. Usually the pricetag runs into the billions. It will often take 10 years from the time you start to develop a new engine until you see a single dime of profit. If you are the board of directors of an engine manufacturer, and you give the greenlight to develop a new product, you might be literally betting the entire company on the success of that new product. So, you have a tendency to be conservative. If you can get a 10% performance improvement from some new never-tried-before fancy contra-rotating fan thingy, or you can get a 5% performance improvement by keeping the same basic tried-and-true design but just tweaking the aerodynamics a bit here and there, you are probably going to go with tried-and-true. Eventually, a limit will be reached where the basic turbofan architecture cannot be tweaked anymore, and then you may see some new thing like this tried, but I don't think we are quite there yet right now.