Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Brother, we really appreciate your question, which shows how interested you are in becoming well acquainted with Islam and its teachings. May Allah bless your efforts in the pursuit of knowledge!
Muslims slaughter animals during `Eid in emulation of Prophet Ibrahim who was about to slaughter his son, Isma`eel, to show obedience to Almighty Allah, when Ishmael was redeemed by a ram brought to Ibrahim by Angel Gabriel. The Angel then conveyed to him Allah's Command to slaughter the ram instead.
With regard to your question, the late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar (may Allah shower mercy on his soul), said:
Slaughtering the sacrifice is better than giving its price in charity, because that was what the Prophet (peace and blessings be upon him) did. Also the sacrifice is an obligation in Islam and if the people turn away from it and give charity instead, they will be guilty of disobeying Allah.
If giving the price of the sacrifice in charity was better than slaughtering the sacrifice, the Prophet (peace and blessings be upon him) would have explained that to his Ummah in word and deed. Indeed, if giving charity was equal to offering the sacrifice, he would have explained that too, because it is easier than going to the trouble of offering the sacrifice. The Prophet (peace and blessings be upon him) never failed to point out the easiest option to his Ummah when it was equal to the more difficult option.
There was a famine during the lifetime of the Prophet (peace and blessings be upon him) and he said, “Whoever among you offers a sacrifice should not keep any of it in his house for more than three days.” The following year, they said, “O Messenger of Allah, should we do what we did last year?” The Prophet (peace and blessings be upon him) said: “Eat, and feed the poor and store some, for last year the people were having a hard time and I wanted you to help them.”
Ibn Al-Qayyim said: “Sacrifice when prescribed is better than giving its price in charity. Hence even if you give many times more the value of the sacrifice for tamattu` and qiran, it will never take its place, and the same applies to udhiyah.”
Excerpted with modifications from: www.islam-qa.com
Read also:
The Concept of Animal Sacrifice in Islam
Appointed to Slaughter a Sacrificial Animal: Can I Cut My Hair?
Offering Sacrifice on `Eid Al-Adha: Obligatory?
Is Islamic Slaughtering Cruel to Animals?
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Allah Almighty knows best.