Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;) and let us consider one another to provoke unto love and to good works: not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching.
Harold Camping admits that Judgment Day is in view here: "We know that Judgment Day is in view in this verse ... ." (source) Mr. Camping is right because we see from the context that the "day" mentioned here is the day of the Lord, the day of judgment:
For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people. It is a fearful thing to fall into the hands of the living God.
Nevertheless, Harold Camping argues that:
Returning to Hebrews 10, verses 24 and 25, we read a very curious comment. Verse 25 declares:(same source)
Not forsaking the assembling of ourselves together, as the manner is...
This is indeed curious language. One would think that it would be more logical to say, "not forsaking the assembling of the congregation" or "not forsaking the assembling of the church." Why does God use the strange language, "assembling of ourselves"? As we have already noted, God is focusing on the time when Judgment Day is very near. We understand this by the phrase, "so much the more, as ye see the day approaching." Another curiosity is the usage of the Greek word episynagogen which is translated "assembling together." This Greek word is used in only one other instance in the Bible. That citation is II Thessalonians 2:1, where we read:
Now we beseech you, brethren, by the coming of our Lord Jesus Christ, and by our gathering together unto him.
The phrase "gathering together" in this verse is translated from the same Greek word episynagogen. When we look at the context of II Thessalonians 2:1, we know who is assembling or gathering together. This passage is speaking of those individuals who are gathering together to meet Christ at his coming. The only people who are ready to meet Christ at his coming are true believers. Churches will not be ready to meet Christ. Whole congregations are not ready to meet Christ. Even if Christ had come before the church age was over, only a remnant of the congregation would have been ready to meet Him.
The point God is making is that the Greek word episynagogen emphasizes the gathering together of individuals. It is not in any way looking at a body of people who are all members of one local congregation.
This agrees with the usage of the same Greek word, episynagogen, which we find in Hebrews 10:25, where God emphasizes that individuals are in view as indicated by the usage of the word "ourselves." Thus, a body of people, like a local congregation, cannot be in view in Hebrews 10:25 any more than a local congregation could be in view in II Thessalonians 2:1.
This argument is absolutely absurd. Allow me to elaborate, though, because my simply saying it is absurd will have little weight with Harold Camping's listeners.
The term "episynagogen" is a word that combines "epi" (a primary preposition that has, in this case, a directional sense) and "sunagoge" (the word from which we derive "synagogue" meaning the meeting or meeting place). To "episunagoge" means to get to synagogue, or to use modern terminology "go to church."
Someone may point out that the term might have a broader sense of simply coming together as an assembly in Greek. While that is true, the context cannot be ignored. This is an epistle to the Hebrews, and must be understood within that context: as being written to Hebrews.
The attempted imposition of the context of 2 Thessalonians 2:1 is also wrong. Even if we understand 2 Thessalonians 2:1 to refer to the gathering unto Christ at the second coming (something of which the church is a foreshadow), that is certainly not the sense that is being used in Hebrews 10:23-25.
We know that it is not the sense of Hebrews 10:23-25, because Hebrews tells us two things:
(1) "as the manner of some is"
While the verb "is" is implied (not stated) in the Greek, the point of the phrase is to compare what the Hebrews should not do with what others have or are doing. But the coming of Christ is not something that has already come, and consequently there would be nothing to which to compare if the sense of "assembling of ourselves together" is a reference to the gathering at the second coming rather than the weekly gathering.
(2) "and so much the more, as ye see the day approaching"
Again, this provides a comparison. The comparison is between the present and the future. This serves to demonstrate that the verse is talking about something that the Hebrew believers were already doing.
It is not just a comparison, but a comparison of enhancement. They are not to get to church less and less as they see the day of the Lord approaching. Instead, they are to assemble more and more. This practice of fellowship is to increase until Jesus' return.
Finally, the argument is absurd because the idea that "ourselves" should be contrasted to "church" is itself absurd. The focus is on the activity of the individuals in going to the assembly. That individual action is contrasted with the action of some people who don't go to church. The usual sense of the text is not that the individuals are supposed to get others to go to church, but that they themselves should go to church.
But I have left out the most obvious argument in the discussion above. The text says:
That means "don't stop." The Greek is "μὴ ἐγκαταλείποντες," which means to leave something behind. We see it used in several places in Scripture:
Acts 2:27 Because thou wilt not leave my soul in hell, neither wilt thou suffer thine Holy One to see corruption.
Matthew 27:46 And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?
Mark 15:34 And at the ninth hour Jesus cried with a loud voice, saying, Eloi, Eloi, lama sabachthani? which is, being interpreted, My God, my God, why hast thou forsaken me?
Romans 9:29 And as Esaias said before, Except the Lord of Sabaoth had left us a seed, we had been as Sodoma, and been made like unto Gomorrha.
2 Timothy 4:10 For Demas hath forsaken me, having loved this present world, and is departed unto Thessalonica; Crescens to Galatia, Titus unto Dalmatia.
2 Timothy 4:16 At my first answer no man stood with me, but all men forsook me: I pray God that it may not be laid to their charge.
Hebrews 13:5 Let your conversation be without covetousness; and be content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee.
As you can see, in every instance it refers to a pre-existing condition that is then either (positively) maintained by the thing remaining, or (negatively) altered by the thing being discontinued. In this case, the pre-existing condition is that the Hebrew believers are going to "synagogue" (first to the synagogue of the Jews and later to the Christian church which corresponds thereto).
The undeniable conclusion is that the author of Hebrews, God himself who inspired it, is telling the Hebrews to continue doing what they were already doing, namely assembling together to worship God. Moreover, God is telling them not to stop doing this but to continue this more and more as the day of judgment approaches. The end of the church age, if we wish to call the New Testament period by that name, is Judgment Day. That day has not yet come, and consequently we are called to continue to assemble together.