I think the biggest point for why the Old Testament isn't as relevant to christians, particularly the laws of Leviticus, is due to the transfiguration of christ.
Christ took on the form of Moses and Elijah, and took over their role, becoming the authority of christianity.
Throwing scripture all over the place won't solve anything, as many modern christians believe that scripture is very much to be taken metaphorically.
And much of the New Testament is just the personal views of varying Christian leaders, such as St Paul, who in his many letters dictates the way the church should be and discusses the teachings of Christ, yet he never met Christ, and became a self declared Apostle only after having a religious experience on the road to Damascus.
To many christians, particularly protestants (and particularly those who are not fundamentalists), the point of christianity is to live your life in a good way, making good choices, worshiping God and Jesus. It's not to read the Bible every single day and adhere to the exact written word of a 2000+ year old book that's been rewritten who knows how many times, and translated from Hebrew, Greek and Latin.
