According to Hindu dharma it is allowed to kill some animal species, but only if it is done in accordance with the strict regulations of the scriptures, as in the sacrifices, as indicated in Manu-smriti and other scriptures.
However cows is explicitly forbidden to kill! There are explicit statements in the scriptures about it:
ācāryaṃ ca pravaktāraṃ pitaraṃ mātaraṃ gurum /
na hiṃsyād brāhmaṇān gāś ca sarvāṃś caiva tapasvinaḥ
Let him never offend (or injure) the teacher who initiated him,
nor him who explained the Veda, nor his father and mother, nor (any
other) Guru, nor cows, nor Brahmanas, nor any men performing
austerities. (Manu smriti 4.162)
In the above quotation from the Manu-smriti expression na hiṃsyād is translated as "never offend" or "never injure". So this verse is an evidence from the scriptures that killing of cows is not allowed!
There is a prayer in the Vishnu Purana 1.19.65:
namo brahmaṇya-devāya go-brāhmaṇa-hitāya ca
My Lord Krishna, You are the well-wisher of the cows and the Brahmanas.
In this verse cows and Brahmanas stand out as especially favored by the Lord, and thus they are especially sacred. Compare this with the above Manu-smriti verse where it is said that some people (Guru, father and mother, teacher who explained the Veda, Brahmanas), and cows should never be killed, and that is because of their special holiness.
It is said in the Bhagavad gita 18.44:
Farming, cow protection and business are the natural work for the
In this verse phrase go-rakṣya was used, which means "cow protection". As we can see from this verse, in the varnashrama dharma cow protection is one of the primary activities. We are not supposed to kill those who we should protect! Right?
It is said in the Srimad Bhagavatam (Bhagavata Purana) 8.19.43 that in time of danger one should be engaged in go-brāhmaṇa-arthe "protecting cows and brahminical culture" (paraphrased).
In the Bhagavatam cows and Brahmanas again stand out in the canto 10, chapter 24 "Worshiping Govardhana Hill" where Lord Krishna encourages his father to perform a sacrifice:
SB 10.24.25: Therefore may a sacrifice for the pleasure of the cows,
the brāhmaṇas and Govardhana Hill begin! With all the paraphernalia
collected for worshiping Indra, let this sacrifice be performed
SB 10.24.29: After everyone has eaten to his satisfaction, you should
all dress and decorate yourselves handsomely, smear your bodies with
sandalwood paste and then circumambulate the cows, the brāhmaṇas, the
sacrificial fires and Govardhana Hill.
SB 10.24.30: This is My idea, O father, and you may carry it out if it
appeals to you. Such a sacrifice will be very dear to the cows, the
brāhmaṇas and Govardhana Hill, and also to Me.
In the above verses we see that the Vedic sacrifice should be done for the pleasure of the Lord Krishna, cows, Govardhana Hill, and Brahmanas!
All of them must be that much especially sacred then.
There are many such verses in the scriptures that speak of a particular sanctity of cows and Brahmanas.