This is a very nit-picky argument. Both the first European universities and Islamic schools of higher learning were part of a tradition of advanced educational institutions dating back as far as there were people to be trained and others to train them. Consider, for example, Plato's Ἀκαδημία (Academy), which operated outside of Athens for roughly three hundred years from the fourth to the first century BCE.^(1) Both early Christian and early Islamic centres of higher learning relevant to this discussion were created for the advancement of specifically religious learning to allow for the education of the clergy: Christians had the cathedral and monastic schools, while Muslims had the madaris (plural of madrasa).^(2) The universities, which began to coalesce around the middle-to-end of the eleventh century with the foundation of such institutions at Bologna and Paris, are directly descended from the earlier cathedral schools (though this is a bit simplified, obviously). In Paris, for example, the local diocesan officials governed the university well after its institutional separation from the Cathedral of Notre-Dame.^(3) It is also important to mention that the papacy was one of the major grantors of university charters during this period, allowing a less formal school to elevate themselves into a university.^(4) The term "university" itself comes from the Latin "universitas," which simply meant "guild" in the context of the period of foundation of which we are speaking.^(5) The universities were, after all, no more than guilds of either teachers (Paris) or students (Bologna) who banded together for mutual benefit, support, and protection, in the sense of a modern labour union.^(6) Jumping ahead a bit, because of numerous factors, including colonialism, industrialization, etc., western culture came to dominate the world, particularly in terms of its modern institutionalization from the eighteenth century to present. During this period, universities were founded all across the globe according to the western pattern, and many pre-western schools--including many large madaris--were reformed to fit this model. The Tunisian University of Ez-Zitouna, for example, was founded as a madrasa in 737 CE, and was reformed into a university in 1956.^(7) With all this in mind, to answer your question, technically universities were invented by Catholics, but they by no means invented schools, and many different kinds of schools predated them all over the world. I hope this helps, and feel free to let me know if you would like me to expand on anything.

​

^(1) Baltes, M. 1993. "Plato's School, the Academy." Hermathena, (155): 5-26.

^(2) Makdisi, George. The Rise of Colleges: Institutions of Learning in Islam and the West. Edinburgh: Edinburgh University Press, 1981.

^(3) Bernstein, Alan E. “Magisterium and License: Corporate Autonomy Against Papal Authority in t the Medieval University of Paris.” Viator 9 (1978), 291-307.

^(4) Hermans, Jos M. M. and Marc Nelissen, eds. Charters of Foundation and Early Documents of the Universities of the Coimbra Group. Leuven: Leuven University Press, 2005.

^(5) Lewis, Charlton T. and Charles Short. A Latin Dictionary. Oxford: Clarendon Press, 1879. The particular entry is viewable here: http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0059:entry=universitas

^(6) Rashdall, Hastings, rev. by F. M. Powicke, and A. B. Emden: The Universities of Europe in the Middle Ages, vol 1. Oxford: Clarendon Press, 1895; 1987.

^(7) For a brief overview of the history of the University of Ez-Zitouna (in French), see their website: http://www.uz.rnu.tn/fr/historique/

​

Edit: References formatted.