I cite; "For 11 centuries Byzantium (not an atheist era...) had not theological schools, not one, while modern Orthodoxy made of faith an object of ‘scientific’ teaching and gives to that teaching the name of Theology, a name that was been kept only for a few saints and fathers – properly speaking, only three of them: St. John (the Evangelist) the Theologian, St. Gregory (Nazianzene) the Theologian and St. Symeon the New Theologian. " This is not true: There are many SCHOLIA, that is explanations and comments, lessons, from Byzantine schoolteachers (SCHOLIA from Latin SCHOLA = school) to most of the Greek authors, from Homer to the Attic orators to the fathers of the Church, such as St. Gregory of Natianze. So there were also schools. Unlickily enough, of those SCHOLIA which regard the Fathers of the Church, have been put in print only a few, and not all, of those regarding St. Gregory of Natianze. It is obvious that they are not used in todays theological schools. In fact the Ortodox Church has adopted in its schools a method of teaching and a kind of learning that is not its own, that is related to the Roman Catholics and that is highly wrong, it is called "scientific", but it is no learning, only an unlearned mystification. In the the past there were highly efficient Schools, todays there is only decay and treason of a glorious heritage.
Scholia are not lessons from school teachers, but comments by bishops, monks, or any church member who had something to say. Were St. Gregory of Nyssa, St. Basil the Great, St. Cyril of Alexandria, St. Maximus Confessor, etc., school teachers?
That in the byzantine ‘university’ there were not theology faculties, is well known and is presented, e.g., in Hans Georg Beck’s, “The Byzantine Millennium”. Modern ‘scientific’ research of theology, as adopted also in Orthodox Churches due to their mimetism of the West, has nothing to do with Byzantine theology, as you also say.
Byzantines let theology be cultivated by whomever wished to think on these matters, without systematic or ‘scientific’ investigation. Thus theology was cultivated mainly by elders for the education of their monks, or by bishops while speaking to people in churches (homilies-speeches). In fact, most of the byzantine commentaries or scholia, such as Chrysostom’s, are speeches to people in the churches during the Liturgy. This is an aspect of the simultaneously social and charismatic character of byzantine life.