Jesus said not to swear to the truth but to simply let our "yes" be yes and our "no" be no. In this world, we accept that people lie and therefore need these markers that this time we are not lying. But in the Reign of God, everyone will simply speak the truth all the time, and so we should move in that direction now.
Matthew 5:33-37
Jesus said to his disciples, ‘Again, you have heard that it was said to those of ancient times, “You shall not swear falsely, but carry out the vows you have made to the Lord.” But I say to you, Do not swear at all, either by heaven, for it is the throne of God, or by the earth, for it is his footstool, or by Jerusalem, for it is the city of the great King. And do not swear by your head, for you cannot make one hair white or black. Let your word be “Yes, Yes” or “No, No”; anything more than this comes from the evil one.
(New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org)