*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:
गुशब्दस्त्वन्धकारः स्यात् रुशब्दस्तन्निरोधकः ।
अन्धकारनिरोधित्वात् गुरुरित्यभिधीयते ॥ 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:
.
न तत्र सूर्यो भाति न चन्द्रतारकं नेमा विद्युतो भान्ति कुतोऽयमग्निः ।
तमेव भान्तमनुभाति सर्वं तस्य भासा सर्वमिदं विभाति ॥ ११ ॥
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
यदादित्यगतं तेजो जगद्भासयतेऽखिलम् ।
यच्चन्द्रमसि यच्चाग्नौ तत्तेजो विद्धि मामकम् ॥ १२ ॥
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 fire 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:
इदं शरीरं कौन्तेय क्षेत्रमित्यभिधीयते ।
एतद्यो वेत्ति तं प्राहुः क्षेत्रज्ञ इति तद्विदः ॥ १ ॥ 13.1
The Supreme Divine Lord said: O Arjun, this body is termed as kṣhetra (the field of activities), and the one who knows this body is called kṣhetrajña (the knower of the field) by the sages who discern the truth about both.
यथा प्रकाशयत्येकः कृत्स्नं लोकमिमं रविः ।
क्षेत्रं क्षेत्री तथा कृत्स्नं प्रकाशयति भारत ॥ ३३ ॥ 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:
अस्तमित आदित्ये याज्ञवल्क्य चन्द्रमस्यस्तमिते शान्तेऽग्नौ शान्तायां वाचि किञ्ज्योतिरेवायं पुरुष इत्यात्मैवास्य ज्योतिर्भवतीत्यात्मनैवायं ज्योतिषास्ते पल्ययते कर्म कुरुते विपल्येतीति ॥ ६ ॥
"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':
किं ज्योतिस्तव भानुमानहनि मे रात्रौ प्रदीपादिकम्
स्यादेवं रविदीपदर्शनविधौ किं ज्योतिराख्याहि मे ।
चक्षुस्तस्य निमीलनादिसमये किं धीर्धियो दर्शने
किं तत्राहमतो भवान् परमकं ज्योतिस्तदस्मि प्रभो ॥
– एकश्लोकी
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:
यो रेतसि तिष्ठन्रेतसोऽन्तरो यं रेतो न वेद यस्य रेतः शरीरं यो रेतोऽन्तरो यमयत्येष त आत्मान्तर्याम्यमृतोऽदृष्टो द्रष्टाश्रुतः श्रोतामतो मन्ताविज्ञातो विज्ञाता नान्योऽतोऽस्ति द्रष्टा नान्योऽतोऽस्ति श्रोता नान्योऽतोऽस्ति मन्ता नान्योऽतोऽस्ति विज्ञातैष त आत्मान्तर्याम्यमृतोऽतोऽन्यदार्तं ततो होद्दालक आरुणिरुपरराम ॥ २३ ॥
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:
श्रीमद्भागवतपुराणम्/स्कन्धः ७/अध्यायः ६
परावरेषु भूतेषु ब्रह्मान्तस्थावरादिषु ।
भौतिकेषु विकारेषु भूतेष्वथ महत्सु च ॥ २० ॥
गुणेषु गुणसाम्ये च गुणव्यतिकरे तथा ।
एक एव परो ह्यात्मा भगवानीश्वरोऽव्यय: ॥ २१ ॥
प्रत्यगात्मस्वरूपेण दृश्यरूपेण च स्वयम् ।
व्याप्यव्यापकनिर्देश्यो ह्यनिर्देश्योऽविकल्पित: ॥ २२ ॥
The same Brahman appears as the jiva and the observed world.
केवलानुभवानन्दस्वरूप: परमेश्वर: ।
माययान्तर्हितैश्वर्य ईयते गुणसर्गया ॥ २३ ॥
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.
कृष्णं वन्दे जगद्गुरुम् 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