In Vedic Dharma, Guru is one who initiates you into the Vedas by giving you the Gayatri Mantra. This Samskara is called the sacred thread ceremony or the Upanayanam.
And in Tantra, Guru is one who relieves you from the ignorance by initiating you into a Mantra. This process is called the Guru Deeksha or the Mantra Deeksha or the Deeksha Samskara. TheAnd the Mantra is called the Guru Mantra.
In Tantra, there are three lines of Gurus : The Divine line (comprised of Gods and Goddesses as Gurus ) , The Enlightened line (comprised of Siddhas or enlightened beings as Gurus ), and the Human line (comprised of human beings as Gurus ).
The enlightened line of Gurus or the Siddhauga Pangti comprises of 11 Gurus viz- Sanaka, Sanananda, Sanatana, SanatkumarSanatkumara, Sanat-Sujata, Dattatreya, Vyasa, Vamadeva etc.
And the disciples of these 6 human Gurus are all the Hindu Gurus that we have in the current world.
Divyaughe ChAdinAthashcha Tacchshaktischa sadAshivaha| Tathpatni Cheswarastasya BhAryA Rudrascha Tadvaduhu|| Vishnushcha TathpriyA
BrahmA TathkanthA DwAdaseritAha|
The Divyauga Guru Pangti consists of 12 namesGurus viz- Adinatha Adinatha, Sadashiva,
Iswara, Rudra, Vishnu and Brahma along with their respective shaktis
or consorts.
Siddhaughe Sanakaishchaba Sanandashcha SanaAtanah| SanatkumArascha SanathsujAtascha Rhibhukshajah|| DattAtreyo Raibtako VAmadevastathaha
Parma| Tato VyAsah Sukaishchava Ekadasha SamiritA||
The enlightened Gurus are 11 in number and they are- Sanaka, Sananda,
Sanatana, Sanathkumara, Sanath-Sujath, Rhibhukshaja, Dattatreya,
Raivataka, Vamadeva & Vyasa.
MAnvaughe Nrisimhashcha Mahesho BhAskara TathA| Mahendro MAdhavo Vishnu Shadethe Cha PrakirtithAha||
The human lines of Gurus consist of six namesGurus namely- Nrisimha, Mahesha,
Bhaskara, Mahendra, Madhava & Vishnu.
KulArnava Tantram, Chapter 6, Verses 64-67.
So, the point is, my badminton teacher is only a badminton teacher but not a Guru in the strict Hindu sense of the word unless he duly belongs to any one of the lineages mentioned above. Similarly for your school teachers.
No, certainly not. In KulArnava Tantram's 13th chapter we find the descriptions of thesuch long lists of qualities that a Guru or SaDSath Guru must possess. One such quality is :
So, needless to say, a very angry person is not fit to be a Guru. Because he is yet to master anger, which is one of the shadaripus.