- This is not clearly* supported in scripture as far as I am aware. In fact, I know scripture says just the opposite in Matthew 5:18 — "For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished." Oh, and if you teach people that even the least (however that is determined) of the laws are not important, you risk your spot in heaven.
Side note: This reminds me that the visitation pastor speaking at my niece's baptism told the parishioners that those laws weren't important to know. Boy did I want to just about scream at that moment! (Which was further instigated by her and the associate(?) pastor discussing whether the number of laws was closer to 600 or 620, to which I really wanted to shout, "There are 613!!!") It's bad enough when churches teach things as fact that contradict scientific knowledge (that particular day it was that "the wind blows wherever it pleases" — in reality, wind blows from cold air masses toward warm air masses); it's a whole nother story when they can't even get their own scripture right!
- Now, you may be able to find contradictions in the Bible (there's a big surprise!), in which case the bigger issue is that the core of the Christian theology of the major denominations in the USA does not support this idea. From the first point, the prior verse (Matthew 5:17) has Jesus claiming he came to fulfill the law. As per Christian theology (including that of the church mentioned in the side note above), Jesus was supposedly a person free of sin who died to serve as punishment for all of us sinning humans. Well, what is "sin"? Basically, a person sins when they violate one of those laws. (If you look at Wikipedia, "sin is the act of violating God's will." But note that the link for "God's will" goes to the article for "Divine law.") So if you claim that the law no longer applies, then a person can no longer sin. Yet, Christian theology teaches that we do still sin. Therefore, the laws must still be in effect.
UPDATE: I was reminded of where the contradictions in the Bible are. I've addressed this in a short post here.
If this argument is so bad, why do Christians use it? I think the answer is twofold. One, people generally don't examine arguments for logical flaws, which allows bad arguments to work. This leads to two, which is that the goal is to find an argument that successfully defends the faith, not one that is logically sound. And the faith requires a defense because many of those laws are absurd (can't eat shellfish is the common example), no longer followed, or it is now recommended that one does the opposite of the law. (Here's one I violated just last week by having my dog neutered: "Not to castrate the male of any species; neither a man, nor a domestic or wild beast, nor a fowl.") Christians know having such laws in the books (see what I did there?) makes their religion look bad. My suspicion would be that Christians have used other excuses to defend the OT laws in the past, but they were less successful than this commonly used excuse that the laws no longer apply and therefore are no longer used.
And what happens when the religious have their logical flaws pointed out to them? Well, they also have handy defense mechanisms against atheists like myself. Typically, ad hominems are unleashed. We are just these bitter atheists who hate their god and are just out to destroy religion (maybe we are even doing the work of Satan), so any argument we make can be ignored,*** logical though it may be. And then they return to their echo chamber of fellow Christians who reinforce their belief that they are not irrational.
* There are likely verses in the New Testament where Jesus is claimed to have said something that contradicts one of those OT laws. I can't think of any specific examples. "Turn the other check" instead of "an eye for an eye" apparently isn't one of them (because "an eye for an eye" is not law). But if there are such verses, I would count them as the contradictions they are and not as evidence that Jesus was doing away with the laws.
** This reminds me that I need to add to my first asterisked note above. I think there are verses in the NT that have Jesus violating OT law. Again, I can't think of any specific examples. But, yet again, these should be counted as the contradictions they are and not as evidence that Jesus was doing away with the laws.
*** The one thing I am actually bitter about, if you could not tell, is being ignored simply for being an atheist.
**** I kind of wish I would have engaged with her on that. But, at the time, I was not intending to have such a conversation (she is the one who brought it up). In hindsight, she is exactly the type of person I need to have such conversations with, because she might not have been able to easily dismiss my argument considering that we had shared political goals (common ground takes the edge off of ad hominems).