How would the law of sacrifice cause sin to abound? The law of sacrifice doesn't cause sin to be magnified.
The law of sacrifice was supposed to be the appeasement of sin. It would cause sin to be atoned for, the exact opposite of what the 10 commandments do.
The 10 commandments is what causes sin to be magnified. How? Because of knowledge. Now all that stuff you didn't even know was sin before, now you know.
Gal 3:19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.
Let's take this verse apart and examine it...
1) Wherefore then serveth the law?
OK, what is the purpose of the Ten Commandments?
Rom 7:7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.
They define sin.
1Jn 3:4 Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
2) It was added because of transgressions
Now transgressions already existed. Can we have trangressions without the Law (the Ten commandments)? No...
Rom 5:13 (For until the law sin was in the world: but sin is not imputed when there is no law.
There is no transgression without Law...
Rom 4:15 Because the law worketh wrath: for where no law is, there is no transgression.
So for transgressions to have existed, the Law must be in force. Cain was told that sin (transgression) lay at the door. If that was the case then Law had to have existed.
What was added because sin was already taking place?
Jer 7:22 For I spake not unto your fathers, nor commanded them in the day that I brought them out of the land of Egypt, concerning burnt offerings or sacrifices:
Yet, God added a Law because people were already breaking Laws. What did He add? He added sin offerings. One example...
Exo 29:36 And thou shalt offer every day a bullock for a sin offering for atonement: and thou shalt cleanse the altar, when thou hast made an atonement for it, and thou shalt anoint it, to sanctify it.
3) till the seed should come to whom the promise was made
How long was the Law of sacrifices? Until Christ came...
Heb 10:1 For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect.
Heb 10:2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.
Heb 10:3 But in those sacrifices there is a remembrance again made of sins every year.
Heb 10:4 For it is not possible that the blood of bulls and of goats should take away sins.
Heb 10:5 Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me:
Heb 10:6 In burnt offerings and sacrifices for sin thou hast had no pleasure.
Heb 10:7 Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God.
Heb 10:8 Above when he said, Sacrifice and offering and burnt offerings and offering for sin thou wouldest not, neither hadst pleasure therein; which are offered by the law;
Heb 10:9 Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second.
Heb 10:10 By the which will we are sanctified through the offering of the body of Jesus Christ once for all.
It is obvious from this that animal sacrifices were not to pay for our sins but rather to point to Christ. They were the schoolmaster to lead us to Christ...
Gal 3:22 But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe.
What promise? The forgivenenss of sin, justification and salvation as outlined in Rom 5:8-10
Gal 3:23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed.
Faith in God for grace was not available to all under the Old Covenant.
Gal 3:24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
Again, back to Hebrews 10:1-10
Gal 3:25 But after that faith is come, we are no longer under a schoolmaster.
After faith in the sacrifice of Christ, we no longer need sacrifices as a yearly reminder that a perfect sacrifice is yet to come, it is a reality...
Heb 10:2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.
Heb 10:3 But in those sacrifices there is a remembrance again made of sins every year.
Heb 10:10 By the which will we are sanctified through the offering of the body of Jesus Christ once for all.
4) and it was ordained by angels in the hand of a mediator.
1Ti 2:5 For there is one God, and one mediator between God and men, the man Christ Jesus;
Heb 9:15 And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
So, the Law that was added was the Law of sacrifices as a reminder that the perfect sacrifice was to come.