Please read the documentation of the time.Parse:
The layout defines the format by showing how the reference time, defined to be
Mon Jan 2 15:04:05 -0700 MST 2006
would be interpreted if it were the value; it serves as an example of the input format. The same interpretation will then be made to the input string.
So the correct format is
t, err := time.Parse("2006-01-02", "2011-01-19")