Good question, but a real answer is lost in the sands of time. Chandradhar Sharma in his work A Critical Survey of Indian Philosophy (https://archive.org/details/IndianPhilosophyACriticalSurvey), chapter entitled Sankhya:
Tradition regards Kapila as the founder of this system. But Sankyha-pravachana-sutra which is attributed to him is generally regarded ...
Well, we have the various Upavedas associated with the four Vedas. Dhanurveda, Ayurveda, Gandharvaveda etc.
There are four Upavedas: Dhanurveda, Gandharvaveda, Ayurveda and
Arthasastra. Some schools hold Sthapatyaveda as the fourth Upaveda
instead of Arthasastra.
Dhanurveda is the science of warfare. Gandharvaveda is the study
if aesthetics ...
Why is killing a brahmin considered sin while killing other caste people is not?
This presupposition is wrong; killing people of other castes is also a sin:
Manusmriti 11.126: One fourth of the expiation for the killing of a Brāhmaṇa has been prescribed for the killing of a Kṣatriya, one
eighth for that of a Vaiśya, and one sixteenth for that of a
Do scriptures specify how animals should be killed during the sacrifice?
Yes, the horse in the Ashwamedha is suffocated with a cloth.
Taittiriya Brahmana 3.9.20:
tArpyeNAshvam samjnapayanti | yajno vai tArpyam | yajnenaivainam samardhayanti | yAmena samnA prastotA'nUpatiSThate | yamalokam evainam gamayati
They (the Samitars, the slaughterers) kill ...
Rig Veda X.72.4 says
Earth sprang from the Productive Power the regions from the earth were
born. Dakṣa was born of Aditi, and Aditi was Dakṣa's Child.
That same Person became Pragâpati (lord of generation). And that
Person which became Pragâpati is this very Agni (fire-altar), who is
now (to be) built.
The question is specifically asking for counter arguments within scriptures that preaches against following a birth based system.
The strongest proof is provided in Manusmriti
3.109 A Brāhmaṇa should not advertise his family and Gotra for the purpose of obtaining a meal. Bragging about these, for the purpose of obtaining a meal, he comes to be called a “...
Chaitra Navaratri starts with pAdyami (1st day) of Chaitra month/mAsa.
King Dasaratha wanted to coronate Sri Rama in chaitra month.
चैत्रः श्रीमानयं मासः पुण्यः पुष्पितकाननः | यौवराज्याय रामस्य
सर्वमेवोपकल्प्यताम् || २-३-४ राज्ञस्तूपरते वाक्ये जनघोषो महानभूत् |
"This is the glorious and auspicious month of Chaitra, in which the
forests bloom ...
The following are the excerpts from the teachings of Sri Ramana Maharshi.
Once ‘A’ asked: How can one be worshipful while engaged in daily work?
Sri Bhagavan did not reply. Ten minutes passed. A few girls came for
darsan of Sri Bhagavan. They began to sing and dance. Their song was
to the effect: “We will churn the milk without losing thought of