There are two types of "elements" that a class can have:
elements (where an element is a field, property, method, event, or delegate)
element is shared by all instances, and is accessed via the class name.
element is unique to each different instance of the class and is accessed via the variable holding the instance reference.
Think about cars for a moment: all cars have a colour - but which colour it is depends on which specific car you are talking about. My car is black; your car is red; this car is green; that car is blue.
is an instance property of the Car class because you need to have a specific instance of a Car in order to ask the question "what colour is it?" - you can't say "what colour is a car?" because it's meaningless without saying which car you mean.
But cars have
properties as well: you can ask "how many wheels has a car?" because all cars have four wheels. (If it had two, it would be a motorbike, not a car)
So if you want to access a List via the class name as in your example, it needs to be common to all instances, i.e. it needs to be
public static List<string> failstudents = new List<string>();