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 this issue, the late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar 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.” (Sunan Abu Dawud)
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.”