Welcome to cruise-chat.
An important thing to know is that all the mainstream cruise lines offer alternate choices for dinner. On the formal nights you can avoid dressing up and simply go to the buffet restaurant for dinner. The casual dinner buffets are very good and usually offer some of the same items being served in the dining room that night. In fact we often hit the dinner buffet at least once on a cruise. You will find this on Carnival, Royal Caribbean, Princess, Celebrity, etc.
Another factor to consider is Carnival has changed their suggested dress codes. Formal has been called "Cruise Elegant" for almost two years, and it no longer requires a coat and tie. You can see more about dress codes at our Dress Code FAQ
Personally I love the new Carnival dress codes. I legally wore shorts to dinner on the casual nights!