The important thing, Jesus is saying (in Matthew 5:33-37), is to tell the truth and keep one's pledges without insisting that a certain form of words must be used if it is to be binding. No oath is necessary for the truthful person... Their word is so reliable that nothing more than a statement is needed from them.
D. A. CarsonSome Christians want enough of Christ to be identified with him but not enough to be seriously inconvenienced; they genuinely cling to basic Christian orthodoxy but do not want to engage in serious Bible study; they value moral probity, especially of the public sort, but do not engage in war against inner corruptions; they fret over the quality of the preacher's sermon but do not worry much over the quality of their own prayer life. Such Christians are content with mediocrity.
D. A. CarsonWhen Christians speak of the authority of Scripture, because Christians believe that this word, even though it's mediated through many different human authors, nevertheless is God breathed and is revealed by God and is utterly reliable and all that it says, with all of its different literary genres, it's trustworthy and without mistake or distortion. It is trustworthy and therefore, because it is from God it has God's authority.
D. A. Carson