The preterists say the following about Matthew 24:34:
One of the meanings of the Greek word translated "generation" is "family":
"genea, a/j, Ion. geneh,, h/j( h`, Ep. dat. geneh/fi: (gi,gnomai): I. of the persons in a family, 1. race, stock, family, Hom., etc.; Pria,mou g. Il.; evk geneh/j according to his family, Ib.; geneh/| by birth-right, Od.; geneh.n Aivtwlo,j by descent, Il.:-of horses, a breed, Ib.:-generally, geneh,n in kind, Hdt.:-also a tribe, nation, Persw/n g. Aesch. 2. a race, generation, oi[hper fu,llwn geneh. toih,de kai. avndrw/n Il.; du,o geneai. avnqrw,pwn Ib. 3. offspring, Orac. ap. Hdt.; and of a single person, Soph. II. of time or place in reference to birth: 1. a birth-place, geneh. evpi. li,mnh| Gugai,h| Il.; of an eagle's eyrie, Od. 2. age, time of life, esp. in phrases geneh/| new,tatoj( presbu,tatoj youngest, eldest, in age, or by birth, Hom. 3. time of birth, evk geneh/j Hdt.; avpo. g. Xen" (Lidell-Scott Greek-English Lexicon).
Now it will now be demonstrated that "family" is the correct translation at Matthew 24:34.
By the Lord Jesus' own admission the "times" and "seasons" have been put in the Father's power (Acts 1:7; Mt.24:36). It is not as if the Lord Jesus had been given a vision in regard to the time when all these things would be fulfilled. Instead, He was the Prophet described here:
"I will raise them up a Prophet from among their brethren, like unto thee, and will put my words in his mouth; and he shall speak unto them all that I shall command him" (Deut.18:18).
The Lord Jesus had no special knowledge in regard to when the things would happen so He certainly would not be pointing out any specific generation of men who would see the signs of which He spoke.
Therefore, the correct translation of the following passage is as follows:
"So likewise ye, when ye shall see all these things, know that it is near, even at the doors. Verily I say unto you, This family shall not pass, till all these things be fulfilled" (Mt.24:33-34).
Of course the "family" refers to the descendants of Abraham, Isaac and Jacob..
The Lord Jesus' sermon in Matthew 24 foretold of the "great tribulation," a time when Israel will be attacked unmercifully in an attempt to destroy the whole family of the Israelites. Therefore it would not be unusual for the Lord Jesus to assure them that they will not be wiped out and that they will continue to exist. Therefore, He told them that the family would still be in existence when He returned to the earth.
In fact, this is not the first time that such assurance had been given to the family of the Israelites, as witnessed by these words:
"Thus says the LORD, Who gives the sun for light by day And the fixed order of the moon and the stars for light by night, Who stirs up the sea so that its waves roar; The LORD of hosts is His name: If this fixed order departs From before Me, declares the LORD, Then the offspring of Israel also will cease from being a nation before Me forever" (Jer.31:35-36).
According to the Lord as long as the sun and moon remain in the sky the offspting of Israel will remain "being a nation" before Him. So there is nothing odd about the Lord Jesus telling the Israelites that "this family shall not pass till all these things be fulfilled," especially with the great tribulation in view.
The ideas of the preterists are based on the assumption that the Lord Jesus would know the time when the great tribulation would happen despite the fact that there is absolutely nothing in the Bible which supports that false idea.