This is because those old Date and SimpleDateFormat are troublesome.
What happens here is that, because hh is used, the number 12 'overflows' to 0 here. The code which actually does this is found in the SimpleDateFormat source code, in the subParse method.
You should use HH. And while you're at it – you should use modern Java Date and Time API from the java.time package:
String startTimeStr = "11:00";
String endTimeStr = "12:00";
LocalTime startTime = LocalTime.parse(startTimeStr);
LocalTime endTime = LocalTime.parse(endTimeStr);
// No need for a explicit formatting string, because the default is used here,
// which is HH:mm[:ss[.nnnnnnnnn]]
if (endTime.isAfter(startTime)) {
    System.out.println("If");
}
else {
    System.out.println("Else");
}
But even if you used an explicit DateTimeFormatter with the pattern string hh:mm, then a DateTimeException would have been thrown because the value to be parsed were ambiguous. 11:00 and 12:00 in a twelve-hour clock could mean two things: either AM or PM. The parser by default doesn't like ambiguous values, so instead of just choosing one and moving on, causing confusion to everyone, the authors decided to immediately stop the parsing process and throw an exception. The following code shows this:
DateTimeFormatter formatter = DateTimeFormatter.ofPattern("hh:mm");
String startTimeStr = "11:00";
LocalTime startTime = LocalTime.parse(startTimeStr, formatter);