3 different ways to add items to the end of a list?

The only reason I can think would be that it depends on what you want as a return value. For instance, you have this array:

arr = [1,2,3]

If you use the :push method, the entire array would be the return value.

arr.push(4)
# returns [1, 2, 3, 4]

But if you did it in the following way, not sure what it's called, you would only get the number you're adding as a return value.

arr[3] = 4
# returns 4

# or

arr[arr.length] = 4
# also returns 4

Since functions, loops and conditional will automatically return the last evaluated value, any of these could be useful depending on the situation. If you want to add something to an array and then tell the person just what they added, the second options are better. But if you want to show someone the whole array after they add something, the :push method is better. Depending on what you want as a return value, you'll end up saving a line or 2 on code by choosing the right one.