Jesus died as a sacrifice for our sins?

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Animal and human sacrifices

Some reasons why humans are sacrificed according to Wikipedia:

• Sacrifice by Indian adherents of Tantrism who believe that human sacrifices to the gods can change their fortune.
• Sacrifice to accompany the dedication of a new building like a temple or bridge. Chinese legends hold that thousands of people were entombed in the Great Wall of China which may be a metaphorical statement, considering the labor and investment of the construction.
• Sacrifice in Aztec and Mayan cultures to the god of fertility to assure good corn harvest.
• Sacrifice of his daughter by a victorious Biblical general Jephthah, and Abraham's near-sacrifice of his son to prove his loyalty to God.
• Sacrifice upon the death of a king, high priest or great leader; the sacrifices were to serve or accompany the deceased leader in the next life. Mongols, Scythians, sometimes Egyptians and various Mesoamerican chiefs could take most of their household, including servants and concubines, with them to the next world. This is sometimes called a "retainer sacrifice," as the leader's retainers would be sacrificed along with their master.
• Sacrifice by ritual combat. Aztecs killed prisoners in ritual combats.
• Sacrifice for divination; a priest would try to predict the future from the body parts of a slain prisoner or slave. According to Strabo, Celts stabbed a victim with a sword and divined the future from his death spasms.
• Sacrifice in times of natural disaster. Droughts, earthquakes, volcanic eruptions, etc. were seen as a sign of anger or displeasure of gods and sacrifices were made to appease the divine ire. Cretans tried to stop the destruction of their island this way.

In the Bible, the Hebrews (modern Jews) beginning from their Father Abraham and other ancient tribes sacrificed animals and humans for their religious purposes. In the time of Moses, the blood of the lamb ensured that the Angel of Death would Passover the Jewish homes and spare their first-born. Much later because of the prevailing beliefs, Jesus came to be regarded as one such human sacrifice, in deference to the pagan practices of the reigning Romans during those periods. 

Does your God delight in someone else suffering and paying for your sins? Would He even be approving of such a repulsive idea? Would this be just and fair to everyone involved? Didn't He decree that everyone shall be held personally responsible and liable for his own thoughts and actions? Did He not through Christ and all the prophets make known His commandments and rules of conduct that we should follow or face the consequences?

Doesn't the Law of Sowing and Reaping apply in this situation? Is it okay for a transgressor to simply confess his sins, admit his fault saying he is sorry and then pray a few Hail Marys, and he will be forgiven?

We all should think again.

Yet today, although this abhorrent practice is much condemned, still, Christians everywhere believe and insist that Christ suffered and died to pay for their sins, releasing them from their accountability.

Where did Jesus teach this in his own words? Or is this simply another misconception and false teaching of mere followers and misguided Biblical writers and editors? What are your thoughts regarding this dogma of the churches?

In fact, Jesus himself was very emphatic when he taught us something else, altogether:

"Seek out the meaning of this particular verse of Scripture, ‘It isn’t your sacrifices and gifts that matter; instead, you must be merciful and kind.’” (MT 9)

"Not everyone who calls me ‘Lord, Lord,’ will enter the Kingdom of Heaven, but only those who do what my Father in heaven wants them to do." (MT 7)

"Settle disputes with your adversary, amicably, before it is too late; otherwise, he might drag you into court and the court would hand you over to the authorities to be thrown in jail. I tell you, you won’t be released from there until you have paid the last penny." (MT 5)

"‘Come, blessed of my Father, inherit the kingdom prepared for you since the creation of the world. For I was hungry and you fed me; I was thirsty and you gave me a drink; I was a stranger and you took me in; naked and you clothed me; sick and in prison and you visited me.’

"Then, the righteous ones will reply, ‘Lord, when did we ever see you hungry and feed you? Or thirsty and give you anything to drink? Or a stranger and help you? Or naked and clothe you? When did we ever see you sick or in prison and visit you?’

"And the King will tell them, ‘When you did this for the least of my brothers, you were doing it for me!’" (MT 25)