We should probably look at the Scriptural source for this idea.
18 And he said: Show me your glory. 19 He answered: I will show you all good, and I will proclaim in the name of the Lord before you: and I will have mercy on whom I will, and I will be merciful to whom it shall please me. 20 And again he said: You can not see my face: for man shall not see me, and live. 21 And again he said: Behold there is a place with me, and you shall stand upon the rock. 22 And when my glory shall pass, I will set you in a hole of the rock, and protect you with my righthand till I pass: 23 And I will take away my hand, and you shall see my back parts: but my face you can not see.
In the beginning was the Word: and the Word was with God: and the Word was God. 2 The same was in the beginning with God. 3 All things were made by him: and without him was made nothing that was made. 4 In him was life: and the life was the light of men. 5 And the light shines in darkness: and the darkness did not comprehend it. 6 There was a man sent from God, whose name was John. 7 This man came for a witness, to give testimony of the light, that all men might believe through him. 8 He was not the light, but was to give testimony of the light. 9 That was the true light, which enlightens every man that comes into this world. 10 He was in the world: and the world was made by him: and the world knew him not. 11 He came unto his own: and his own received him not. 12 But as many as received him, he gave them power to be made the sons of God, to them that believe in his name. 13 Who are born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. 14 And the Word was made flesh and dwelt among us (and we saw his glory, the glory as it were of the only begotten of the Father), full of grace and truth. 15 John bears witness of him and cries out, saying: This was he of whom I spoke: He that shall come after me is preferred before me: because he was before me. 16 And of his fullness we all have received: and grace for grace. 17 For the law was given by Moses: grace and truth came by Jesus Christ. 18 No man has seen God at any time: the only begotten Son who is in the Bosom of the Father, he has declared him.
Philosophically, I’d think it’s got something to do with the fact that knowledge of anything is, or is like, the possession of that thing’s form in the intellect. (The passage probably means ‘seeing’ in the mind.) God’s “full form” is Himself, Whom is infinitely greater than our tiny minds. If we tried to fit all of God into our heads, then, well, they’d burst. Also, to know a thing is seemingly to, in a sense, become that thing, or to become indivisibly one with it.
One example might be when you “know her in the Biblical sense.” When a man “knows” a woman by uniting with her in the act of sex, the two become “un-divorcably” one, “two in one flesh,” – a new form, a “rebirth” of them in the offspring. For another (better) example, consider various passages from Aristotle’s De Anima:
-The thinking part of the soul must therefore be, while impassible, capable of receiving the form of an object; that is, must be potentially identical in character with its object without being the object. Mind must be related to what is thinkable, as sense is to what is sensible.
-Therefore, since everything is a possible object of thought, mind in order, as Anaxagoras says, to dominate, that is, to know, must be pure from all admixture;
-speculative knowledge and its object are identical;
-the soul is in a way all existing things;
-for existing things are either sensible or thinkable, and knowledge is in a way what is knowable;
-Within the soul the faculties of knowledge and sensation are potentially these objects, the one what is knowable, the other what is sensible. They must be either the things themselves or their forms. The former alternative is of course impossible: it is not the stone which is present in the soul but its form.
If so, man’s attempt to fully see and know God in all His infinite glory is insanely proud. It would be like a foolish grasp at His power, to overcome His throne and dominate Him – to be God himself. This is the greatest sin; it will destroy us. (If per impossibile it happened, we would literally become nothing, since we would then be what necessarily cannot exist, the impossible.)
Looks like Garrigou-Lagrange addresses the topic well here:
to say that created intelligence can, solely by its own natural powers, positively and properly know the divine essence, Deity in itself, can even see that essence without medium, is equivalent to saying that the created intellect has the same formal object as has the uncreated intellect. And that is the same thing as to say that the intellective creature has the same nature as uncreated intelligence, that is, is God Himself. But a created and finite God is an absurdity