What a wise person (jnani) knows directly – can be summarized in below Adi Shankaracharya's words.
Which is why there is NO GAIN for a jnani to argue or defend themselves – when challenged by criticism of an ignorant Jīva (person who identifies “I” with Body-Mind complex):
Brahman means “Non-changing Consciousness / Awareness / Existence“. They are all synonyms in context of Brahman (the Supreme Reality).
Irony is everyone is looking for the Supreme Reality, yet everyone already IS the Supreme Reality, including you – whether acknowledged or denied.
Just like whether Gravity's presence/existence is known or unknown – it's still in operation – and doesn't care about your knowledge of it.
In fact, the only reason why you can comfortably argue Gravity's presence – is because it's safely keeping you on the ground. Good luck contemplating existential questions while flying off into the sky. 🙂
Similarly, Brahman is known to you – whether you acknowledge or deny it's presence/existence.
How is it known?It's known as self-evident “I”.
Now you say “Prove it to me!“…
You can't deny your EXISTENCE. You can't deny that you are AWARE. Doesn't matter what you're aware of (thought, emotion, doubt, peace).
Point is, you are still AWARE.
The “AWARENESS” is Brahman.
Therefore Chandogya Upanishad states mahavakya (a great saying that compresses lots of wisdom into a single statement), “Tat Tvam Asi”. Meaning, “You are THAT”.
Meaning, you can not, NOT be Brahman. Because Brahman is “AWARENESS”.
And when are you not AWARE?
Deep sleep? (Most common objection)
What is your experience of Sleep? You'll either say (a) Nothing, or (b) Blissful.
How do you know it's nothing/blissful?
If Awareness wasn't present in Deep Sleep, you wouldn't even know what I'm talking about. You'd say “I don't sleep! I only dream!“.
And when you say “I'm going to sleep“, do you mean “I'm going to dream“? No!
In fact you'd be reluctant going to bed knowing there will only be Dream.
You go to bed gladly because there is knowledge about that state of nothingness-bliss.
Which obviously means there is AWARENESS OF nothingness-bliss.
Thus AWARENESS (Brahman) is present even in Deep Sleep.
“The universe is false.”
“False” does NOT mean “Illusion” or non-existent, as often used by dualists as bases of attack against Advaita Vedanta's methodology.
False just means: Changing. Or incidental. We call this Mithya.
Important point to know is the truth of Mithya is the unchanging reality called Satyam (Brahman). Thus Mithya enjoys it's dependence on Satya. While Satya is independent of Mithya. Meaning, Satya-Mithya are never apart. They are not two (Advaita).
(See below Wave, Ocean, H2O analogy to see relationship between Satya-Mithya. Although you need a Vedanta teacher for full explanation of this. Because revealing Truth has many facets and can't be effectively passed through text alone.)
Coming back to principle of changing…
Where is the little 5 year old “you” NOW? Gone! (Mithya)
It was real back then. But now you probably don't even relate to that 5 year old child.
So was the child real? Yesand no.
Yes, while the child was a child.
No, as the child died (changed) to give way to the adult.
But what remained throughout the child AND adult experience? Awareness. YOU. “I”.
That's because Satyam is unchanging, unceasing Awareness.
“The jīva (individual self) is, indeed, Brahman, not another.”
Simple analogy we often use in Vedanta…
Jīva (person) is wave of Ocean.
Ocean is Īśvara (God).
H2O is Brahman.
What permeates both Wave (Jīva) and Ocean (Īśvara)? H2O (Brahman).
Meaning there is only H2O (Brahman).
LINE 2:
“By this should be known the Truth of the scripture. Thus is the drum-beat of Vedanta.”
When Truth, as revealed in FIRST line, is comprehended – then knowledge of Scripture (Śruti) becomes known and comprehensible. Instead of mysterious and contradictory.
But to get to stage of comprehension, you need to be taught by a teacher/guru. Else Scriptures will only become an intellectual exercise, lacking depth of their INTENDED meaning.
Line 1 is the essence of Advaita Vedanta's message.
PSYCHOLOGICAL REASON:
Jīva is insecure. Meaning they don't like aspects regarding either their body, mind or intellect.
These aspects are unconsciously projected onto every other human. Including saints.
Thus no matter how saintly a saint is, the jīva finds faults in them (mainly “This person is ignorant, unenlightened!”), just like any other person in the society.
What's more, why do you think dead-guru's are so popular in the spiritual world? Why do so many love Ramana Maharshi, when his body-mind-intellect is long gone?
Because the ignorant jiva who never met someone, automatically projects positive qualities. Same story with Jesus or any wise person of the past.
But the moment the jiva meets a living saint, then jiva mostly sees another ignorant/unenlightened/faulty person.
Interesting, isn't it. We respect dead saints who've we've never met. And disrespect those who are right infront of us. And when they too die, they too will be respected by next generation who never met them. Etc.
For this reason, wise person doesn't bother arguing. They may attempt to demonstrate a point to help align jīva's mind to the scriptures. But whether the jīva will listen is totally out of everyone's hands, including God's (metaphorical) hands.
Wow that is very good. Simple to the point. BAM! There has always been an I going all the way back i feel it. Like watching a river flowing i have periodically been “pulled in” to the “drama of the river” twisting turning,churning etc. And moments of “sobriety” where i am simply watching it detached. Its a struggle between the two it seems. In and out . In and out.
How is it known? It's known as self-evident “I”.
False just means: Changing. Or incidental. We call this Mithya. 
Jīva (person) is wave of Ocean.
When Truth, as revealed in FIRST line, is comprehended – then knowledge of Scripture (Śruti) becomes known and comprehensible. Instead of mysterious and contradictory.
Wow that is very good. Simple to the point. BAM! There has always been an I going all the way back i feel it. Like watching a river flowing i have periodically been “pulled in” to the “drama of the river” twisting turning,churning etc. And moments of “sobriety” where i am simply watching it detached. Its a struggle between the two it seems. In and out . In and out.