In most Bibles, Matthew 24:34 says something like:
“...this generation will not pass away until...”
However, ours says:
“...this people won’t pass away until...”
The word usually translated as generation from the Greek can indeed mean that, but not always; it can just mean family or a group of people. The actual meaning depends on the context. Usually it does indeed mean generation in the Greek Christian books.
The Aramaic texts also use a word with the same ambiguity: sha’urbetah. It can just mean family, or a distinct class of people. For example, the priestly class. It could be translated as family, tribe, people, or nation. However, unlike the Greek, only the plural version can mean generations.
So strictly-speaking, the Aramaic version of Matthew 24:34 does not say generation, but something more like nation or people.
Also, in the Aramaic of Matthew 24:30, the word is usually translated as tribes:
‘...the Son of Man’s sign will appear in the skies, and all the tribes of the earth will beat themselves...’
Now, if the Aramaic text accurately reflects Jesus’ words, and Jesus wanted to specifically mean a generation (a group of people who are living at the same time), he could have used the word darah which actually means generation. Yet he did not.
That word appears in other parts of the Aramaic New Testament in contexts that clearly point to a time-limit (e.g. Ephesians 3:5; Hebrews 3:10). However, the Aramaic texts of Matthew 24:34 don’t use that word, they use the singular sha’urbetah which means only family, tribe, people, or nation.
For this reason, our version of Matthew 24:34 says ‘people’ and not ‘generation.’
This is also why our version of the parallel account in Mark 13:30 (from the Greek text) uses the definition of ‘people,’ as its the only definition shared by both the Aramaic and Greek words.