The philosophical conceprt of "comprehension" and the so-called principle of comprehension has its source in traditional logic.
See Port Royal Logic:
[for] Port-Royal [...] the significance of general ideas has two aspects: the comprehension [la comprehension] and the extension [l'étendue]. The comprehension consists in the set of attributes essential to the idea. For example, the comprehension of the idea ‘triangle’ includes the attributes extension, shape, three lines, and three angles. The extension of the idea consists in the inferiors or subjects to which the term applies, which for Port-Royal includes “all the different species of triangles”.
See: Antoine Arnauld et Pierre Nicole, La logique ou l'art de penser (3eme ed, 1668), page 69.
Following the Scottish philosopher William Hamilton, in his Logic, page 59, the distiction has been reformulated as that between intension and extension:
the Internal Quantity of a notion, its Intension or Comprehension, [and] the External Quantity of a notion or its Extension.
Consider the well-kown traditional example : "every Human is Mortal".
We read it today in terms of classes (or sets), i.e. estensionally, as meaning that the set of Humans is a subset of the set of Mortals.
But we can also read it intensionally as asserting that attribute of Mortality is contained into the concept of Humanity.
Thus, a concept is "made of" attributes : its intension (or comprehension), and to a concept corresponds the class of objects to which the concept applies (the objects "falling under" the concept) : its extension.
The comprehension principle is the principle asserting that we can use the attributes defining a concept (its intension) in order to carve out from the universe of objects the collection of all and only those objects to which the concept applies (its extension).
In order to understand your misconception, you have to go back to the French origins of the word, comparing two different meanings of the same term :
Compréhension : la compréhension d'un concept est la donnée des concepts plus généraux qui peuvent en être prédiqués, et peuvent entrer dans sa définition; là où l' extension d'un concept est la classe (l'ensemble) des individus qui répondent à ce concept.)
Compréhension : est un processus psychologique lié à un objet physique ou abstrait tel que la personne, la situation ou le message selon lequel une personne est capable de réfléchir et d’utiliser des concepts pour traiter cet objet de manière appropriée.
Both derive from Latin comprehensiō, comprehensiōnem, from comprehendere (“to grasp”), from the prefix com- + prehendere (“to seize”).