Nowadays, Universities are coed. With this fact in mind, I have read Pius XI encyclical Divini Illius Magistri and he said something about coeducation.

 What is the reason, in laymen's terms, that he spoke so strongly against coeducation?

If men and women work closely together in school they will be distracted by those of the other sex and also tempted to fornicate.

Men and women reason differently.

Men and women reason differently.

Well, at the age in question, it's doubtful whether either reasons at all! Girls "reason" with their giggly girl friends, and boys "reason" with the tip of the male organ. Both groups need to get accustomed, through disciplined instruction in a controlled environment, to the idea of reasoning with the gray matter inside their noggin. Neither group profits from the distraction of having the other around during school hours. They have plenty of opportunities for essential (not even to mention nonessential) social contact outside the classroom.

From Pope Pius XI's Divini Illius Magistri on Christian education:

68. False also and harmful to Christian education is the so-called method of "coeducation." This too, by many of its supporters, is founded upon naturalism and the denial of original sin; but by all, upon a deplorable confusion of ideas that mistakes a leveling promiscuity and equality, for the legitimate association of the sexes. The Creator has ordained and disposed perfect union of the sexes only in matrimony, and, with varying degrees of contact, in the family and in society. Besides there is not in nature itself, which fashions the two quite different in organism, in temperament, in abilities, anything to suggest that there can be or ought to be promiscuity, and much less equality, in the training of the two sexes. These, in keeping with the wonderful designs of the Creator, are destined to complement each other in the family and in society, precisely because of their differences, which therefore ought to be maintained and encouraged during their years of formation, with the necessary distinction and corresponding separation, according to age and circuмstances. These principles, with due regard to time and place, must, in accordance with Christian prudence, be applied to all schools, particularly in the most delicate and decisive period of formation, that, namely, of adolescence; and in gymnastic exercises and deportment, special care must be had of Christian modesty in young women and girls, which is so gravely impaired by any kind of exhibition in public.