Why did God send his son to the cross?

First off, it was not a cross. The cross was a symbol of false religious worship, a long time before Jesus even gave his life. To obtain the truth, and get accurate knowledge, a person must follow this direction from the Scriptures - Acts 17:11 . . . carefully examining the Scriptures daily to see whether these things were so. - - - - Because that is where the truth is found - John 17:17 - Sanctify them by means of the truth; your word is truth. - - - - So, you can do some research on the cross here (but remember to examine the Scriptures closely)

https://www.jw.org/en/search/?q=cross

Because before Adam and Eve was created God the Father and Jesus Christ sat down and made a plan what to do if Adam and Eve threw sin a poisonous substance into the genetic gene pool. Jesus made the agreement with God that if this happens that Jesus would become the antidote. So when it happened God put into the chain of events. A method by which Jesus could put back the antidote in order to let life freely flow back from God to man after the safety gate slammed shut when Adam introduced the poison into the genetic pool

God sends you and me also to the cross, the problems with all of us is that we are not that sensitive to what God wants from us and we have become expert in avoiding responsibility for our spiritual development.

You should read the Bible to understand the Christian faith.

John 3:16

For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.

You should buy yourself a Holy Bible and start by reading the first four books of the New Testament (Matthew, Mark, Luke and John Gospels)