*Everyone is a 'Jagadguru' by default* *!!*
There is a popular verse on the etymology of the word 'Guru':
Here is a reference from the Advaya taaraka upanishad. This verse is there in the Guru Gita too:
рдЧुрд╢рдм्рджрд╕्рдд्рд╡рди्рдзрдХाрд░ः рд╕्рдпाрдд् рд░ुрд╢рдм्рджрд╕्рддрди्рдиिрд░ोрдзрдХः ।
рдЕрди्рдзрдХाрд░рдиिрд░ोрдзिрдд्рд╡ाрдд् рдЧुрд░ुрд░िрдд्рдпрднिрдзीрдпрддे ॥ 16॥
The verse is cited in the commentary to the Vivekachudamani verse 15 by HH Sri Chandrashekhara Bharati Swamin and the reference is Gurugita 1.34.
The syllable 'gu' represents darkness, The syllable 'ru' represents its remover. Because (the Guru) removes darkness (of ignorance), He is called 'Guru'.
Although this verse is about the ignorance pertaining to oneself and its removal, the theme - of removal of darkness pertaining to the whole creation in the mechanism of perception is adapted here.
The Upanishads and the Bh.gita say that the Atman-light is responsible for the illumining of the world which is by itself inert/insentient/jaDa. It needs the sentient agent to illumine it and thereby make known itself to the perceiver.
Mundakopanishat 2.2.11:
.
рди рддрдд्рд░ рд╕ूрд░्рдпो рднाрддि рди рдЪрди्рдж्рд░рддाрд░рдХं рдиेрдоा рд╡िрдж्рдпुрддो рднाрди्рддि рдХुрддोрд╜рдпрдордЧ्рдиिः ।
рддрдоेрд╡ рднाрди्рддрдордиुрднाрддि рд╕рд░्рд╡ं рддрд╕्рдп рднाрд╕ा рд╕рд░्рд╡рдоिрджं рд╡िрднाрддि ॥ резрез ॥
The sun does not shine there, nor the moon and the stars, nor these lightnings, not to speak of this fire. When He shines, everything shines after Him; by His light everything is lighted.
Bhagavad gita: 15.12
рдпрджाрджिрдд्рдпрдЧрддं рддेрдЬो рдЬрдЧрдж्рднाрд╕рдпрддेрд╜рдЦिрд▓рдо् ।
рдпрдЪ्рдЪрди्рдж्рд░рдорд╕ि рдпрдЪ्рдЪाрдЧ्рдиौ рддрдд्рддेрдЬो рд╡िрдж्рдзि рдоाрдордХрдо् ॥ резреи ॥
The splendor of the sun, which dissipates the darkness of this whole world, comes from Me. And the splendor of the moon and the splendor of ямБre are also from Me.
Thereby it is conveyed that the ultimate illumining agent is Brahman/Atman.
In the 13th chapter of the Bh.Gita we have a couple of verses that emphatically say that it is the Atman that illumines the world:
рдЗрджं рд╢рд░ीрд░ं рдХौрди्рддेрдп рдХ्рд╖ेрдд्рд░рдоिрдд्рдпрднिрдзीрдпрддे ।
рдПрддрдж्рдпो рд╡ेрдд्рддि рддं рдк्рд░ाрд╣ुः рдХ्рд╖ेрдд्рд░рдЬ्рдЮ рдЗрддि рддрдж्рд╡िрджः ॥ рез ॥ 13.1
The Supreme Divine Lord said: O Arjun, this body is termed as kс╣гhetra (the field of activities), and the one who knows this body is called kс╣гhetraj├▒a (the knower of the field) by the sages who discern the truth about both.
рдпрдеा рдк्рд░рдХाрд╢рдпрдд्рдпेрдХः рдХृрдд्рд╕्рдиं рд▓ोрдХрдоिрдоं рд░рд╡िः ।
рдХ्рд╖ेрдд्рд░ं рдХ्рд╖ेрдд्рд░ी рддрдеा рдХृрдд्рд╕्рдиं рдк्рд░рдХाрд╢рдпрддि рднाрд░рдд ॥ рейрей ॥ 13.33
Just as the one sun illuminates the entire world, so too does the Lord of the field (Supreme Self/the Atman) illuminate the entire field, O Arjuna.
The Brihadaranyaka Upanishad, JyotirbrahmaNam, 4.3.6 gives the essence:
рдЕрд╕्рддрдоिрдд рдЖрджिрдд्рдпे рдпाрдЬ्рдЮрд╡рд▓्рдХ्рдп рдЪрди्рдж्рд░рдорд╕्рдпрд╕्рддрдоिрддे рд╢ाрди्рддेрд╜рдЧ्рдиौ рд╢ाрди्рддाрдпां рд╡ाрдЪि рдХिрдЮ्рдЬ्рдпोрддिрд░ेрд╡ाрдпं рдкुрд░ुрд╖ рдЗрдд्рдпाрдд्рдоैрд╡ाрд╕्рдп рдЬ्рдпोрддिрд░्рднрд╡рддीрдд्рдпाрдд्рдордиैрд╡ाрдпं рдЬ्рдпोрддिрд╖ाрд╕्рддे рдкрд▓्рдпрдпрддे рдХрд░्рдо рдХुрд░ुрддे рд╡िрдкрд▓्рдпेрддीрддि ॥ рем ॥
"When the sun has set, Yajnavalkya and the moon has set and the fire has gone out and speech has stopped, what serves as light for a man?" "The self, indeed, is his light, for with the self as light he sits, goes out, works and returns."
This is what is captured by Shankaracharya in the famous 'Eka shloki':
рдХिं рдЬ्рдпोрддिрд╕्рддрд╡ рднाрдиुрдоाрдирд╣рдиि рдоे рд░ाрдд्рд░ौ рдк्рд░рджीрдкाрджिрдХрдо्
рд╕्рдпाрджेрд╡ं рд░рд╡िрджीрдкрджрд░्рд╢рдирд╡िрдзौ рдХिं рдЬ्рдпोрддिрд░ाрдЦ्рдпाрд╣ि рдоे ।
рдЪрдХ्рд╖ुрд╕्рддрд╕्рдп рдиिрдоीрд▓рдиाрджिрд╕рдордпे рдХिं рдзीрд░्рдзिрдпो рджрд░्рд╢рдиे
рдХिं рддрдд्рд░ाрд╣рдорддो рднрд╡ाрди् рдкрд░рдордХं рдЬ्рдпोрддिрд╕्рддрджрд╕्рдоि рдк्рд░рднो ॥
– рдПрдХрд╢्рд▓ोрдХी
What is the source of light for you? To me, during the day, it is the lofty sun; at night, it is the lamp and the like. Let it be so. Tell me, in seeing the sun and the lamp, what is the source illumination? O, that is the eye! What then, when the eyes are closed? O, it is the intelligence! All right. What reveals the intelligence – its functions? Ah, coming to that, it is my own Self, the 'I'! Well, your own Self is then the supreme brilliance, the ultimate light, the first and the last source of illumination! Is it not? Yes, O Lord, it is so – "I am That".
The Antaryami Brahmana of the Brihadaranyaka Upanishad says: 3.7.23:
рдпो рд░ेрддрд╕ि рддिрд╖्рдарди्рд░ेрддрд╕ोрд╜рди्рддрд░ो рдпं рд░ेрддो рди рд╡ेрдж рдпрд╕्рдп рд░ेрддः рд╢рд░ीрд░ं рдпो рд░ेрддोрд╜рди्рддрд░ो рдпрдордпрдд्рдпेрд╖ рдд рдЖрдд्рдоाрди्рддрд░्рдпाрдо्рдпрдоृрддोрд╜рджृрд╖्рдЯो рдж्рд░рд╖्рдЯाрд╢्рд░ुрддः рд╢्рд░ोрддाрдорддो рдорди्рддाрд╡िрдЬ्рдЮाрддो рд╡िрдЬ्рдЮाрддा рдиाрди्рдпोрд╜рддोрд╜рд╕्рддि рдж्рд░рд╖्рдЯा рдиाрди्рдпोрд╜рддोрд╜рд╕्рддि рд╢्рд░ोрддा рдиाрди्рдпोрд╜рддोрд╜рд╕्рддि рдорди्рддा рдиाрди्рдпोрд╜рддोрд╜рд╕्рддि рд╡िрдЬ्рдЮाрддैрд╖ рдд рдЖрдд्рдоाрди्рддрд░्рдпाрдо्рдпрдоृрддोрд╜рддोрд╜рди्рдпрджाрд░्рддं рддрддो рд╣ोрдж्рджाрд▓рдХ рдЖрд░ुрдгिрд░ुрдкрд░рд░ाрдо ॥ реирей ॥
This Upanishad says that the 'I' that we say in the experiences 'I see, know...' is none other than the immanent Brahman, Antharyami.
This is what Prahlada says in the Bhagavata as 'Pratyagatma':
Prahlada, teaching his fellow daitya students, says these words:
рд╢्рд░ीрдордж्рднाрдЧрд╡рддрдкुрд░ाрдгрдо्/рд╕्рдХрди्рдзः рен/рдЕрдз्рдпाрдпः рем
рдкрд░ाрд╡рд░ेрд╖ु рднूрддेрд╖ु рдм्рд░рд╣्рдоाрди्рддрд╕्рдеाрд╡рд░ाрджिрд╖ु ।
рднौрддिрдХेрд╖ु рд╡िрдХाрд░ेрд╖ु рднूрддेрд╖्рд╡рде рдорд╣рдд्рд╕ु рдЪ ॥ реиреж ॥
рдЧुрдгेрд╖ु рдЧुрдгрд╕ाрдо्рдпे рдЪ рдЧुрдгрд╡्рдпрддिрдХрд░े рддрдеा ।
рдПрдХ рдПрд╡ рдкрд░ो рд╣्рдпाрдд्рдоा рднрдЧрд╡ाрдиीрд╢्рд╡рд░ोрд╜рд╡्рдпрдп: ॥ реирез ॥
рдк्рд░рдд्рдпрдЧाрдд्рдорд╕्рд╡рд░ूрдкेрдг рджृрд╢्рдпрд░ूрдкेрдг рдЪ рд╕्рд╡рдпрдо् ।
рд╡्рдпाрдк्рдпрд╡्рдпाрдкрдХрдиिрд░्рджेрд╢्рдпो рд╣्рдпрдиिрд░्рджेрд╢्рдпोрд╜рд╡िрдХрд▓्рдкिрдд: ॥ реиреи ॥
The same Brahman appears as the jiva and the observed world.
рдХेрд╡рд▓ाрдиुрднрд╡ाрдирди्рджрд╕्рд╡рд░ूрдк: рдкрд░рдоेрд╢्рд╡рд░: ।
рдоाрдпрдпाрди्рддрд░्рд╣िрддैрд╢्рд╡рд░्рдп рдИрдпрддे рдЧुрдгрд╕рд░्рдЧрдпा ॥ реирей ॥
Residing in the body it is this Brahman that is known as 'Antharyami' and is said to be the Pratyagatma (innermost self) that lends sentience to the senses and mind. Knowing this Entity correctly leads to liberation.
The purport:
From all the above pramANa-s we conclude that the Atman light is the one that removes the darkness pertaining to the world and illumines it thereby enabling the perception of objects. Thus the Atman is the Guru - remover of the darkness - pertaining to the Jagat and thereby Jagadguru in this sense. Every sentient being, jiva, has this capacity to illumine the entire creation through the medium of the mind and the sense organs. In the above cited Bh.Gita couple of verses, the important message of 'knowing is illumining' is conveyed.
рдХृрд╖्рдгं рд╡рди्рджे рдЬрдЧрдж्рдЧुрд░ुрдо् In fact in the above cited Bh.Gita 15th ch. verse, the Lord says that it is He, His light of Consciousness, that illumines the entire creation. And that happens through the medium of the jivAtman. This jivAtman is taught in the Upanishads and the Bh.Gita 13.2 to be none other than the Paramatman, Brahman.
Om Tat Sat