I studied physics and maths in Germany where such failure rates (50% in the first exam, 90% in the make-up exam) were common. I also organised one first-semester physics course with similar failure rates in the exams. Finally, I attended many exam corrections as a tutor. I will limit my self to these subjects, though I am quite confident that my answer also holds for others.
Relevant aspects of the German academic system
- German students pick a field of study when entering university.
- Studying is essentially free in Germany.
- As a result, universities do not treat students as customers.
- In many fields, including maths and physics, there is no admission cut-off by high-school grades (“Numerus Clausus”) or only a very lenient one.
- There is a considerable number of “eternal” students who unsuccessfully study a subject for many years before eventually dropping out.
As a result, everybody who completed high school (Abitur) can enrol in such programmes.
Also see this answer of mine.
Why do many students fail?
The drop-out rates for students of maths and physics are rather high in Germany. There are several reasons for this and not all are good, but in my experience, the following are predominant:
At a university level, these subjects are quite different from their school counterparts. The level of abstraction and speed is higher. Many students encounter proofs for the first time at university.
Students are required to work much more independently at university. If they decide not to do anything at all, nobody will reprimand them quickly.
Exams (and exercises) focus much more on understanding and being able to apply things than memorisation and blindly applying methods.
In my estimate, roughly half the students who begin studying physics or math are just not in the right field of study and have no chance of completing the programme, no matter how well the courses and exams are designed. (A considerable portion of these realises this very early and never writes a single exam.) On top, there are many students who need a few semesters to get the hang of studying.
Why it is accepted that many students fail?
Due to the above reasons, there are no good predictors of whether somebody succeeds studying. For example, some students who excel at school maths are completely unsuited for studying mathematics and cannot know before they actually study it. Conversely, entrance restrictions for these fields would keep away some excellent students who have struggled with the school system (I know some of these).
Therefore, the best way to tell whether somebody is really suited to study maths or physics is to let them do it.
As a result you get many students who fail exams, in particular in the first semesters.
Why not let more students pass?
The general idea is that students who fail an exam missed the rudimentary goals of the course and will only have more trouble with advanced courses (which are considered to be even harder). Therefore it will be best for them to repeat the course or drop out. Yes, the course might have been didactically bad or similar, but even then, there is no benefit to let students pass to make up for that. In particular, you do not want that students graduate who have not learnt what they should, as it devalues the degree and causes all the problems people doing jobs they are not qualified for.
I witnessed and participated in some discussions around setting fail–pass thresholds for exams with different people. The main focus was always whether all people who would pass the exam had met the minimal goals of the course, not on whether the right amount of people passed or similar.
In “my” exam, the vast majority of students who failed made a series of fundamental mistakes that indicated a severe lack of understanding. For example, many used energy conservation to solve a problem with explicit and unknown friction. Mind that this was a fully open-book exam, so skills like memorising played hardly any role. I acknowledge that some people were suffering from examination anxiety and were failing due to other issues, but I am quite confident that most people who failed the exam had no chance of ever obtaining a physics degree (at least one that wasn’t completely worthless). Also, a considerable portion of students failing this first-semester course had already been studying for years.
In physics, another aspect is that often only students who passed their first exam may enter the lab courses, which require more resources per student, in particular students who put in no effort whatsoever and may break things as a result. By contrast, another student in a lecture with exercises costs almost nothing.
What about the second exam?
If both exams are equally difficult, a 90% failure rate in the second exam indicates that the exams are fair and have a reasonable difficulty. If exam success completely depends on luck, you would expect the failure rates to be the same for both exams.
By contrast, if most students who bring in the requirements for the course and put in the effort pass the first exam, mostly “bad” students remain for the second exam and those are more likely to fail. Of course, you also have students who were sick for the first exam, had a bad day, or really made an effort between the exams and those make up the 10% that pass the second exam.
I also witnessed some cases where both exams were badly designed and focussed on different skills and topics than the exercises or common sense would let you expect. Here the pass rates in the second exams was much higher because then everybody was prepared for what the exam designer was throwing at them.
Reverse example: medicine
In Germany, access to medicine programmes is highly restricted. You essentially need to finish high school (Abitur) with the best possible grade or wait very long or meet pre-conditions such as having worked as a nurse, etc. Also, the contents of the field are less abstract, etc. People tend to joke that the entrance criteria for medicine capture exactly the skills required for studying medicine, namely blind memorising and similar (and unfortunately these skills are less relevant for practising medicine). As a result, drop-out rates for medicine programmes are much lower and the mentioned failure rates may cause a ruckus.