What were the typical arguments against women's higher education in XIX century Germany?

A student that cannot binge drink? Never!

Also from Treitschke. Used to dismiss Hildegard Wegscheider when she wanted to listen to his lectures.

The above quote in the question is recorded in the memoirs of Helene Stöcker, who shared a similar fate asking permission to be a visiting reader to his lectures.

In Prussia the women's desire for higher education first came up around 1865 and remained largely hypothetical for a whole generation, whose males regarded that generally as just a "crazy idea". While a few individual women were allowed to visit the lectures (but not take any exams or earn any grades, usually^*), they were almost all again excluded eventually until 1880. Formal immatriculation than went state by state from 1900–1909.

Before 1909 there were altogether around 3000 woman who wanted to study at universities, compared to 53300 male students in 1909 alone.

The German university system was by 1890 in a type of crisis that overlapped in many ways with class, religion, nationality and gender. It had to expand and did expand and the old authoritarian elites didn't like what they saw. Up and coming low lives in their eyes, taking away or at least inflating the former prestige that a degree conferred. Not only women, but also working class men, Russians, Poles and Jews flocking in. That's the perfect storm for misogynistic, antisemite, anti-non-German in general conservatives.

Friedrich Paulsen wrote a few student handbooks that describe the typical qualities expected from a student:

1. Maturity (a quality generally denied to most women, but especially the young ones. Plus a problem of formality. This maturity was generally proven by acquiring an Abitur, in German also called Reifezeugnis "certificate of maturity". Not easy to come by for a woman in the first place)
2. Emancipation, from the family (again, unthinkable for women)
3. (academic and personal) freedom at the university (we don't want that for women)
4. A certain sense of honour (to be defended when challenged with a sword. Mensur for women?).

As is evidenced by the argumentative strategies that the feminists of the day employed, the male part of the academic elite feared the competition of women as well. The women's rights activists emphasised that they wanted to open up universities mainly for middle class women that needed the higher education mainly for using these spoils in 'womanly' jobs, like nurses, doctors, children's teachers.

Most remarkably, the central argument that was given when women were finally allowed to be immatriculated was that by formalising it and at the same time insisting on applicants being in possession of an Abitur, that this would reduce the number of women generally, and especially non-German women. (Althoff, 1905 [GSAPK, Rep. 76 Va Sekt. 1 Tit. VIII Nr. 8 Bd. XI, 195-197])

*: Not the only, but one very notable exception is Sofia Kowalewskaja. Never seen as a Russian, but feared for her womanhood and mental acuity, just outclassing way too many males.

Treitschke is one example of the widespread extremism, chauvinism, antisemitism of those days. Within these circles, among them Adolf Stoecker, all of the above quote can be seen as more than typical. It's literally a stereotypical attitude prevailing at the time. Less extreme men against women's higher education still had reservations as they summarily dismissed women as being intellectually inferior to men and not meant to be even in those spheres that were designated as belonging to men.

The above is an attempted summary of a recent study: Patricia Mazón: Gender and the Modern Research University The Admission of Women to German Higher Education, 1865-1914, Stanford University Press: Stanford, 2003.

Going closer to actual sources would be: A supposedly mostly neutral evaluation of woman in German academia is found in this 1897 book. It gives the views of 100 professors – for and against, as the preface states – at the time on that topic.

Arthur Kirchhoff: "Die akademische Frau : Gutachten hervorragender Universitätsprofessoren, Frauenlehrer und Schriftsteller über die Befähigung der Frau zum wissenschaftlichen Studium und Berufe", Hugo Steinitz Verlag: Berlin, 1897 (PDF).

Most seem in favour, with varying lists of conditions attached. One naysayer would be Emil Warburg, p257, who lists horrible examples of failures, like in Oxford, where several women studied medicine but even fewer were indeed practicing, as "they were physically too weak"

The Astronomer Wilhelm von Bezold p258 displays even some anger to have been asked about that at all. Women should only be doctors, at the utmost, as this would fall into their nature.

By the end of the 19th century the conservatives were already a sizeable minority. But like Planck observed, progress comes only one funeral at a time. The most prevailing arguments still circulating around 1900 were thus:

• Women do not need to work, they are will be provided for by their husbands.
• Their nature his that they will be wives and mothers anyway.
• Competition by women will lower the wages, even of men, thus women will deprive themselves of a suitable provider in yet another way.
• Studying has detrimental influence on the physical body and health, especially for women.
• Women are weak. Women are intellectually incapable of studying.
• We just don't want that. Learned women are a violation of our ideal of German femininity.
• The pedagogical methods are unsuitable for women's education.
• Nice looking women will distract the male students.

Those arguments may sound somewhat familiar even today. But the conservative stance is best exemplified by Wüstenfeld, who, asked for his arguments for or against 'women at the universities', just answered:

At the age of 88, I had to use the help of others to write my letters, and I can only express my opinion in general terms, that for the admission of women to academic studies and consequently to employment in subjects requiring a learned education, I am strongly against it. (Kirchoff, p225, emphasis copied from there.)