Why do Christians Worship on Sunday instead of Saturday?

Because of the tradition of the Roman Catholic Church, who claim it is founded “not of scripture, but on tradition” and that “Protestants ought to keep their Sabbath on Saturday”:

Catholic Record
Sunday is founded, not of scripture, but on tradition, and is distinctly a Catholic institution. As there is no scripture for the transfer of the day of rest from the last to the first day of the week, Protestants ought to keep their Sabbath on Saturday and thus leave Catholics in full possession of Sunday.

Catholic Record, September 17, 1893.

The Bible tells us to never put “tradition of men” instead of Christ:

Colossians 2:8 King James Version (KJV)
8 Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ.

Jesus asked the people why they “transgress the commandment of God by your tradition”:

Matthew 15:3 King James Version (KJV)
3 But he answered and said unto them, Why do ye also transgress the commandment of God by your tradition?

Jesus Christ kept the Sabbath every week:

Luke 13:10 King James Version (KJV)
10 And he was teaching in one of the synagogues on the sabbath.

The Sabbath day is identified in the Bible as the day after Jesus died and was laid in a sepulchre, called today “Good Friday”, so the Sabbath day must be Saturday, which they kept “according to the commandment”:

Luke 23:52-56 King James Version (KJV)
52 This man went unto Pilate, and begged the body of Jesus.
53 And he took it down, and wrapped it in linen, and laid it in a sepulchre that was hewn in stone, wherein never man before was laid.
54 And that day was the preparation, and the sabbath drew on.
55 And the women also, which came with him from Galilee, followed after, and beheld the sepulchre, and how his body was laid.
56 And they returned, and prepared spices and ointments; and rested the sabbath day according to the commandment.

The day that they “found not the body” of Jesus was the “first day of the week”, the day known today as “Sunday” or “Easter Sunday”, when the women returned with the “spices which they had prepared”:

Luke 24:1-3 King James Version (KJV)
1 Now upon the first day of the week, very early in the morning, they came unto the sepulchre, bringing the spices which they had prepared, and certain others with them.
2 And they found the stone rolled away from the sepulchre.
3 And they entered in, and found not the body of the Lord Jesus.

God himself rested from creating on the “seventh day” of the week:

Genesis 2:2-3 King James Version (KJV)
2 And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made.
3 And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made.

The Sabbath day Saturday will be valid until the end of time, with Jesus telling us to “pray ye that your flight be not” “on the sabbath day” in the “great tribulation”, such as was not since the beginning of the world “nor ever shall be”:

Matthew 24:20-21 King James Version (KJV)
20 But pray ye that your flight be not in the winter, neither on the sabbath day:
21 For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor ever shall be.