Deadlines are tight. The scope is ever changing. We just don't have time to write tests. It's more important to get functionality out the door. We've all been there. Whatever the case may be, sometimes you will find yourself working on a project that was not written with testing in mind.
There never seems to be enough time to do it right, but there's always time to do it over.
So, what are the issues you might face that would prevent you from adding tests to a legacy application?
When a system wasn't written with testing in mind, it can be quite difficult to go back and add tests at a later date. Classes with concrete dependencies and tight coupling make software applications difficult to test. Things such as large classes and functions, Law of Demeter violations, global state, and static methods can also make for a system that can be very difficult to test.
Much like building a house by starting with a shaky foundation, untestable code begets untestable code. Unless pieces of the system can be decoupled from the rest of the application, the untestable trend will likely continue, and often does.