Are humans really superior to other animals or are they equal?
A society invariable attaches superiority of X over Y when X has more value than Y conforming to what the society values. As an instance, if a society values entertainment owing to its shoddy escapes from drudgery of daily life, then entertainers shall have more value than other citizens however it may brag about superficial equality, fraternity, justice & all the rest of it. So, superiority or inferiority is an affect of inequality, i.e., inequality is the cause whereas superiority or inferiority is an effect.
Since inequality is a factual reality that one is more intelligent that another; one is more kind than another, etc., the concept of superiority has to come into existence as a fact.
Human beings having more capacity in terms of all the 4 Puruṣārtha (Puruṣārtha that Sanātana dharma values) than animals obviously are superior than animals. Sanātana dharma being expression of factuality shall also consider human beings superior over animals.
But while Sanātana dharma admits the factuality of superiority of human beings over animals, it also sheds light on factuality of them being the part of the same Brahman & their relevance in its (Brahman's) outpouring as evident from Frog-Hymns of Rigveda Book 7, mount of devatā-s, etc. to the extent that humans are supposed to even worship them once in a while as found in various scriptures like Chānḍogya Upaniṣad section 2,
अजा हिंकारोऽवयः प्रस्तावो गाव उद्गीथोऽश्वाः प्रतिहारः पुरुषो निधनमेता रेवत्यः पशुषु प्रोताः ॥ २.१८.१ ॥
ajā hiṃkāro'vayaḥ prastāvo gāva udgītho'śvāḥ pratihāraḥ puruṣo nidhanametā revatyaḥ paśuṣu protāḥ || 2.18.1 ||
- Goats are the hiṃkāra, sheep are the prastāva, cows represent the udgītha, horses are the pratihāra, and a human being is the nidhana. The Sāma called Revatī is established in animals.
So, whilst SD accepts the factuality of human beings being superior to animals, it also throws light on their equal relevance in existence.
I do not recall seeing any such discussion in the Rig Veda Samhita (translator: Griffiths) or in Sam Veda and Yajur Veda Samhitas (translator: Devi Chand).
I do not recall seeing any such discussion in the Gita or the Upanishads.
The idea that humans are superior to others is there in the Mahabharata .
The swan [Brahman] said, ‘I disclose unto you a great mystery. There is no status that is superior to that of humanity. Freed from sin like the Moon from the murky clouds, the man of wisdom, shining in resplendence, attains to success by patiently waiting for his time. A person of restrained soul, who becomes the object of adoration with all by becoming the foremost of the supporting pillars of the universe, and towards whom only agreeable words are spoken by all, attains to the companionship of the deities.’
Mahabharata Santi Parva Section CCC
The concept that human birth is a rare thing is there in other spiritual writings. I have given one example below.
There are three things which are rare indeed and are due to the grace of God - namely a human birth, the longing for liberation, and the protecting care of a perfected sage.
Vivekacudamuni 3 translated by Swami Madhavananda