Why do our sages say that the very latest time for Moshiach's arrival is 6,000 years after creation?
In a sense, a thousand years are equivalent to one day in the eyes of G-d, as is written in Psalms (90:4), "A thousand years in Your eyes are like a day that passes." Therefore, the six millennia since creation are compared to the six days of creation. It is written in Talmud (Rosh Hashana 31a): "For six thousand years the world will exist" (meaning, that it will exist in its present state, before the coming Redemption).
Chassidic teachings explain that the six thousand years (and the six days of creation) correspond to six spiritual attributes.
The first thousand years correspond to the attribute of Kindness--goodness in free-flowing abundance. Therefore, during that period people lived very long lives, as the Torah attests.
The second thousand years correspond to the attribute of Severity. During that era, most of humanity and life on earth was wiped out by Noah’s flood.
The third millennium corresponds to the attribute of Beauty--the combination of kindness and severity together. During this era the Torah was given, which includes both positive and negative mitzvot.
The fourth millennium corresponds to the attribute of Netzach--victory, or eternity. The two Holy Temples stood during this era, eventually to be replaced by a third, which will stand forever. As our sages say, "Eternity--this is Jerusalem."
The fifth millennium, the attribute of Hod, Glory, is an offshoot of severity. This was a time of deep exile and harsh struggles, as is written in Daniel: "My glory has been turned into destruction."
The sixth millennium, corresponding to Yesod, Foundation, represents the establishment of all the six attributes. During this millennium will be the final preparation and the culmination of all previous millennia--for the time known as "a day that is all Shabbat," the era of Moshiach.
Had we been worthy, we would have been redeemed in the beginning of the sixth millennium, since even a small portion of it could have sufficed. As our sages say (Sanhedrin 98b), "If they are worthy--I will hasten it." However, being that we have already passed the midpoint, and more precisely, the three-quarter point of the 6th millennium, it is already "high time" for Moshiach's coming.
Maamarei Admur Hazaken, Parshiyot, p. 419.