Very simply, the answer to this question is that Christians are under a different law from the law that Israel was under.  Israel was under the Law of Moses given by God to Israel at Mt. Sinai (Exodus, chapters 19-31).  This law continued in force until Jesus Christ died on the cross (Colossians 2:14).  Jesus was an Israelite.  The Law of Moses was in effect during His lifetime.  Therefore, He kept the Law of Moses in order to be faithful to God.  This explains why Jesus worshipped in the synagogue on the sabbath.  The Law of Moses taught:  Remember the Sabbath day to keep it holy.  Six days you shall labor and do all your work, but the  seventh day is the Sabbath of the Lord your God (Exodus 20:8-10).  So He came to Nazareth, where He had been brought up.  And as His custom was, He went into the synagogue on the sabbath day, and stood up to read (Luke 4:16).

While Jesus lived on earth, He kept the Law of Moses and taught others to do so.  In the Sermon on the Mount, Jesus said:  Do not think that I came to destroy the Law or the Prophets.  I did not come to destroy but to fulfill.  For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled (Matthew 5:17,18).  Please notice that Jesus said nothing would pass from the Law “till all is fulfilled.

Jesus  fulfilled all that was written in the Old Testament – the Law, the Psalms, and the Prophets.  Then He said to them, ‘These are the words which I spoke  to you, while I was still with you, that all things must be fulfilled, which were written in the Law of Moses, and in the Prophets, and in the Psalms concerning Me’” (Luke 24:44).

The purpose of the Law which was given to Israel at Mt. Sinai, the Law of Moses, is clearly seen in the book of Galatians.  What purpose then does the Law serve?  It was added because of transgressions, till the Seed should come to whom the promise was made; and it was appointed through angels by the hand of a mediator” (Galatians 3:19). The Law was to be in effect “till the Seed should come.” The promised Seed was Jesus Christ (Genesis 3:15; 12:1-3; Galatians 3:16).

Please notice again, “Therefore the Law was our tutor to bring us to Christ, that we might be justified by faith.  But after faith has come, we are no longer under a tutor (Galatians 3:24,25).  If we are no longer under the Law of Moses, then obviously the Sabbath law is not binding upon us today.

When did the Law of Moses as a law binding upon God’s people end?  The answer is, it ended when Jesus died on the cross thus fulfilling it.  Please notice:  But now in Christ Jesus you who once were far off have been brought near by the blood of Christ.  For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace” (Ephesians 2:13-15).    Jesus abolished the law of commandments (the Law of Moses which included the command to keep the sabbath, Exodus 20:8).  He abolished it “in His flesh;” that is by His death on the cross (cf. Colossians 2:14-17).

The new law, the Law of Christ, came into effect on Pentecost Day (Acts 2).  On that day, the church of Christ was established (Acts 2:36-47).  From that time, we find Christians meeting to worship upon the first day of the week which is Sunday.  Now on the first day of the week, when the disciples came together to break bread, Paul, ready to depart the next day, spoke to them and continued his message until midnight (Acts 20:7).  On the first day of the week let each one of you lay something aside, storing up as he may prosper, that there be no collections when I come  (I Corinthians 16:1, 2).

In summary, why do Christians meet for worship on Sunday, the first day of the week, instead of Saturday, the seventh day of the week?  The teaching of the Bible is plain.  The Law of Moses, which included the sabbath commandment, was to the nation of Israel only.  It lasted as a binding law until Christ died on the cross.  The Law of Christ, which began at Pentecost, is God’s law for all mankind today.  The Law of Christ teaches that we are to meet on Sunday, the first day of the week.  This is the day upon which our Lord arose from the dead (Matthew 28:1; Mark 16:2-6; Luke 24:1; John 20:1).  The day upon which the church began, Pentecost day, also was on the first day of the week (Leviticus 23:9-16).  Therefore, we can see why the Lord chose the first day of the week as the day of worship for Christians.