Your code has two logic problems:
- self.list.index(index) in self.listdoesn't do what you think it does, the index won't be in the list, the word may be
- self.list.pop(index)would pop- index, but it expects an actual index, which is not what you're passing to the method
Your code also suffers from horrible naming. To make a point, here's an almost working version of your code with your naming scheme dialed to 11:
class List:
    def __init__(List, list):
        List.list = list
    def List(List, index):
        if List.list.index(index) > -1:
            List.list.pop(List.list.index(index))
        else:
            print("The value isn't in the list.")
list = List(["list", "List", "LIST", "list "])
list.List("list")
print(list.list)
list.List("not in list")
Output:
['List', 'LIST', 'list ']
Traceback (most recent call last):
  File "F:\Project\Python\sandbox_310\my_list.py", line 15, in <module>
    list.List("not in list")
  File "F:\Project\Python\sandbox_310\my_list.py", line 6, in List
    if List.list.index(index) > -1:
ValueError: 'not in list' is not in list
Here's a more reasonably named version, that catches the exception, so it works as you expect:
class MyList:
    def __init__(self, xs):
        self.xs = xs
    def delete(self, x):
        try:
            self.xs.pop(self.xs.index(x))
        except ValueError:
            print("The value isn't in the list.")
example = MyList(["green", "blue", "yellow", "brown"])
example.delete("green")
print(example.xs)
example.delete("no")
Output;
['blue', 'yellow', 'brown']
The value isn't in the list.
And here's a streamlined version, which no longer throws an exception (because it checks whether it can remove before trying to do so, and not calling .index() which causes the error as well):
class MyList:
    def __init__(self, xs):
        self.xs = xs
    def delete(self, x):
        if x in self.xs:
            self.xs.remove(x)
        else:
            print("The value isn't in the list.")
example = MyList(["green", "blue", "yellow", "brown"])
example.delete("green")
print(example.xs)
example.delete("no")
Of course, you could also just:
class MyList(list):
    def safe_remove(self, x):
        if x in self:
            self.remove(x)
        else:
            print("The value isn't in the list.")
example = MyList(["green", "blue", "yellow", "brown"])
example.remove("green")  # MyList *is* a list, so all standard methods work
print(example)
example.safe_remove("no")  # but using the added safe_remove, you get what you want
Result:
['blue', 'yellow', 'brown']
The value isn't in the list.