>>Why in the old Testament did people feel the need to sacrifice animals to God? Was this only done before Jesus came?<<
People in the Old Testament sacrificed animals because God instructed them to do so and accepted them from their hand. Some illustrations include Abel (Gen. 4:4; Heb. 11:4), Noah (Gen. 8:20-21) and Abraham (Gen. 22:12-14). When God gave the nation of Israel a distinct law at Mount Sinai, it contained a great deal of instruction about animal sacrifices (see Exo. 29:38-46; the book of Leviticus).
One of the central purposes of the animal sacrifices under the Law of Moses was to keep before the eyes and hearts of Israel their sin and the truth that life had to be given in order for their sins to be forgiveness (Heb. 9:22; 10:3).
There was a problem, though: "It is not possible that the blood of bulls and goats could take away sins." (Heb. 10:4) Therefore, the animal sacrifices of the OT law of Moses were repeated over and over (Heb. 10:1-3, 11).
This leads to your next question:
>>Was this only done before Jesus came?<<
Yes, animal sacrifices were only properly offered to God before the death of Jesus on the cross. Once His blood was shed, it was offered before God, opening the way to heaven for all who believe (Heb. 9:11-12; 10:19-20).
The animal sacrifices of the law of Moses were a foreshadowing of the perfect and complete sacrifice of Jesus Christ for the sins of the world (see Heb. 9:13-14; 10:1). If animal sacrificed had perfected the worshipper, no more would have been needed nor offered. Yet, there was continual shedding of animal blood under the law of Moses (Heb. 10:2-3, 11).
This is not true of the sacrifice of Jesus, who offered Himself one time for all
time for the sins of the world. Hebrews 10:10-14 emphatically states:
10 By that will we have been sanctified through the offering of the body of Jesus Christ once for all.
11 And every priest stands ministering daily and offering repeatedly the same sacrifices, which can never take away sins.
12 But this Man, after He had offered one sacrifice for sins forever, sat down at the right hand of God,
13 from that time waiting till His enemies are made His footstool.
14 For by one offering He has perfected forever those who are being sanctified.
Note especially verse 12, which says Jesus offered "one sacrifice for sins forever." His sacrifice on the cross was sufficient to forever pay the price of redemption for sinners (Eph. 1:7; 1 Pet. 2:24).
Animal sacrifices served their purpose well. They taught man of his need to be purified from his sins by the giving of life (please see Lev. 17:11). But now, the law of Moses, which contained regulations for animal sacrifice, has been "nailed to the cross" (Col. 2:14).
It was the life of the Son of God, given up freely on the cross once, that forever has the power to remove sin (Heb. 9:25-28). The gospel of Christ, which contains the provisions of the sacrifice of Christ, brings salvation to all who will believe and obey Him (Rom. 1:16-17; Heb. 5:8-9).
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