No man knoweth the day or hour
Harold Camping's followers believe that Christ's return can be accurately predicted from the bible and they believe that God has revealed that date to Camping and themselves. They are wrong, of course, because there is a serious flaw in the way that Camping interprets the bible.
Scripture clearly says "no man knoweth the day or hour". If Christ does return on May 21, Camping's calculations will only be a coincidence. The bible does not tell us when Christ will return, and God's revelation to us (the bible) is complete. That means God does not continue to reveal more to us that what He has already chosen to reveal in the bible.
I can't say Christ won't return on May 21, but I don't think it is likely. In fact, if you consider the vision in Daniel 2, Christ's return could still be many thousands of years in the future. The critical understanding from the bible is to always be ready, because you don't know when Christ will return.
This is not the first time Camping has predicted a date. That alone qualifies him as a false prophet, according to Deuteronomy:
21"And if thou say in thine heart, How shall we know the word which the LORD hath not spoken?
22When a prophet speaketh in the name of the LORD, if the thing follow not, nor come to pass, that is the thing which the LORD hath not spoken, but the prophet hath spoken it presumptuously: thou shalt not be afraid of him."
Consider Matthew 24:3, Jesus' disciples ask two questions. Jesus' answers continue long into Chapter 25. Pay the most attention to the second answer and it's point.
Question 1: "When shall these things be?"
The "things" the diciples are talking about are the things Jesus had just spoke about (in the previous chapter, Mat 23, and continuing into Mat 24:1-2), speaking of the literal destruction Jerusalem and of the temple. Jesus answers this first question in Mat 24:4-35, and gives many indicators and warnings about it's timing. From outside historical references we know that Jerusalem was destroyed and the temple torn down around AD 70. That fits with the timeline given by Jesus in Mat 23:36 "...All these things shall come upon this generation", and again in Mat 24:34, "This generation shall not pass, till all these things be fulfilled." In other words, Jesus said that those things would happen in their lifetime (not 2,000 years later).
Question 2: "What [shall be] the sign of thy coming, and of the end of the world?"
Jesus addresses this second question starting with Matthew 24:36 and continues through chapter 25:46. 24:36 begins with a new paragraph in the original Greek and notice the transition from talking about "these things" to "that day". The obvious principle from Mat 24:36 and following, is "always be ready". The warning is not "Jesus will come on such and such date" nor "God will reveal the date in due time," rather we are specifically warned that Jesus will come at a time not expected therefore always be diligent in what you are supposed to be doing. If Christians knew the time of Christ's return, then His return would be expected not "in such an hour as ye think not" (Mat 24:44). You are instructed to always be prepared so that you will not be found unprepared.
In other words, even if Camping's calendar were accurate, his conclusion and prediction are certainly wrong because discovering the date in advance is impossible.