All Praise to Allah Subhanahu wa Taala and blessings of Him be on Prophet Muhammad peace be upon him His family and companions,
Praying Taraweeh in the Mosque is Sunnah ,If someone prays at home he would miss those rewards of praying in congregation but he would not be sinful.So it is not obligatory to offer taraweeh at Mosque but is Sunnah.
'Abdur Rahman bin 'Abdul Qari said, "I went out in the company of
'Umar bin Al-Khattab one night in Ramadan to the mosque and found the
people praying in different groups. A man praying alone or a man
praying with a little group behind him. So, 'Umar said, 'In my opinion
I would better collect these (people) under the leadership of one Qari
(Reciter) (i.e. let them pray in congregation!)'. So, he made up his
mind to congregate them behind Ubai bin Ka'b. Then on another night I
went again in his company and the people were praying behind their
reciter. On that, 'Umar remarked, 'What an excellent Bid'a (i.e.
innovation in religion) this is; but the prayer which they do not
perform, but sleep at its time is better than the one they are
offering.' He meant the prayer in the last part of the night. (In
those days) people used to pray in the early part of the
night."(Bukhari)
Now because Prophet Muhammad peace be upon him said to hold fast to his Sunnah and Sunnah of the rightly guided Caliphs so Ahlus Sunnah strongly believe to follow their way based on this Hadith :
'Irbad bin Sariyah (May Allah be pleased with him) reported: One day,
Messenger of Allah (ﷺ) delivered a very effective speech, as a result,
eyes shed tears and hearts became softened. A man said: "O Prophet of
Allah! It sounds as if this is a farewell speech, so advise us." He
(ﷺ) said, "I admonish you to fear Allah, and to listen and obey even
if a black slave has been appointed as your leader. For whoever among
you lives after me will see much discord. So hold fast to my Sunnah
and the Sunnah of the Rightly-Guided Caliphs who will come after me.
Adhere to them and hold fast to them. Beware of Bid'ah (in religion)
because every Bid'ah is a misguidance." [Abu Da wud and At-Tirmidhi].
That is why it is recommended by All scholars that is a confirmed Sunnah and also praying in congregation has more rewards but still would not be considered as Fardh.
It was narrated from Ibn 'Umar that the Messenger of Allah (ﷺ) said:
"Praying in congregation is twenty-seven times better than praying
alone."(Nasai)
Also see this Fatwa:
Imam Haskafi (Allah have mercy on him) states:
“The Tarawih prayers are an emphasized Sunna, due to the continued practice of the rightly guided Caliphs, for both men and women… It is a communal Sunna (sunna ala ‘l-kifaya), however, [for men] to perform them in congregation according to the sounder opinion. As such, if the [entire] community of the Mosque abandoned the congregation, they would all be sinful, unless if only some members of the community abandoned it [in which case no one will be sinful]. And any prayer for which congregation is prescribed; it is more virtuous to perform that prayer in the Mosque.”
As for performing Tarawih prayers in congregation in the Mosque, it is a communal Sunna for men. As such, if one offers Eisha Salat in congregation and then performs Tarawih on his own at home, he would miss out on the immense rewards for praying in congregation in the Mosque but it will not be sinful, blameworthy or disliked even with persistence.
Allah Swt and His Messenger knows best.
Source :Here