Postmillennialism is the doctrine that says that, before his second coming, Christ will establish clear outward supremacy amongst the nations, for a prolonged period of time (likely to be centuries at least). Not all people will be converted, but you will be able to say that "the nations have been converted"; the nations in general (or perhaps all of them) will acknowledge that Jesus is Lord, and will order themselves to live under his rule, and will willingly and gladly effectively abolish competing ideologies from public expression. In other words, the gospel's visible triumph is of the sort that means it comes to outwardly dominate over all other alternative beliefs, clearly and conspicuously, throughout the earth.
Postmillennial theologians routinely describe the attractions of their belief in terms of it being a theology of "hope" or "optimism"; a theology that means that we can live in this world with hope/expectation, and know that our labour is not in vain in the Lord. Other views are said to be pessimistic, depressing, lacking hope, and draining their adherents of motivation to serve Christ today.
One - in my view, fatal - problem with this description is that the New Testament clearly teaches Christians that they can, indeed must, live with hope, and know that their labour is not in vain in the Lord, upon different grounds. We look forwards with joy and expectation, because Christ has conquered sin and death, sat down at God's right hand, rules over all things, and is coming again in glory. That is to say, the New Testament explicitly provides other grounds for hope, and portrays those other grounds as entirely sufficient for the outlook that postmillennial theologians say that we need their doctrine in order to arrive at.
Or in other words again, in the New Testament outlook, we live with hope because of the gospel of Christ's death and resurrection, and return. Throughout, the accomplishments of Christ through his cross and empty tomb, through which the dark powers have been defeated, are declared by Christ's messengers to his people as the grounds of their joy and hope; and the culmination of these things is in his second coming to which we look forward with eagerness, as the night will soon be past and the dawn is at hand.
Inasmuch as postmillennial theologians tell us that it is the further announcement (if we, for the sake of argument, grant that this announcement is made somewhere) of the certainty of Christ's clear victory over opposing ideologies consisting in the (vast?) majority of people abandoning them that we find joy, hope, and reason to work for him, they have an irresolvable problem, which is as follows. Either the reasons that the apostles everywhere emphasised were a mistaken emphasis, or they were insufficient reasons for our rejoicing, or the extra reasons provided by postmillennialism are unnecessary.
i.e. We have the horns of a dilemma. Upon one horn, the constant New Testament emphasis upon hope, joy and victory in Christ's resurrection and return was apparently not enough. Any and all passages in which this reason is given need further supplementing by other reasons, and the apostles were mistaken to leave out those reasons in those passages. Christ's ascension and return are, apparently, only enough to rejoice in if you also supply the missing "in between" that during the period from one to another, the proportion of those who will voluntarily submit to him will also reach the threshold that postmillennialism requires (it is not enough that he has a representative number that cumulatively, across the ages, when assembled from across all their different tribes and countries, is the vast Revelation 7 multitude). Or alternatively, upon the other horn, it was enough, meaning that in fact we already have a "theology of hope" without having to accept the beliefs of postmillennialism. Postmillennialism is either false or redundant. Inasfar as you base your joy upon belief about what percentage will be converted before Christ's return, you fail to base your joy upon a foundation that Paul, Peter et. al. already saw as fully sufficient, and you either miss out, or you hold that they were incorrect to do so.
It is my view that a comprehensive study of what excited and motivated the apostles in their preaching and teaching reveals that postmillennialism answers a question that didn't interest them, and which they didn't teach anyone to ask, and which they would have highlighted as a mistaken question if someone had decided to. "Will the greater part of humanity be saved?" belongs to the category of things that God has chosen not to reveal and which are not our business. It is not for us to know the numbers and seasons which God has set in his own sovereignty. On the other hand, certain other spiritual realities, the dawning of the last times through the resurrection and exaltation of Christ, were entirely transformative for the outlook of the apostles and those whom they taught. Those things are revealed, and make all the difference. They make all the difference: they are what constitute the grounds of our certain hope of glory. Anyone who teaches that we must work in a certain way because God has revealed what proportion of humanity will in future recognise him during a substantial period of time teaches people to place their hope somewhere other than where we're meant to put it, and damages the spiritual lives of the hearers. He teaches them to not make his primary way of looking at reality to be the "two realms" scheme of the New Testament (the old realm of Satan, sin and death, and the new realm, which has already invaded history, of Christ, resurrection and life).
False motivations - ones which didn't interest the authoritative declarers of Jesus Christ and his will for his people at all, and which teach people to look at history and space-time reality using a different fundamental lens to that of the New Testament - are not good things, and are not indifferent things. It's not OK to say "oh, but wouldn't it be wonderful if it were true?" We are not called to be wise above what is revealed. It is not wonderful to decide to self-consciously adopt such a viewpoint as ones fundamental outlook on reality. God didn't make a mistake with the viewpoint that he told us to adopt. But here is another fatal problem for advocates of post-millennialism. If they can't say "you should adopt this set of beliefs, because it will give you hope and optimism for the future" (since it's clear from the Bible that we're already meant to have that for other reasons), then what can they say? What now is the marketing point to get people excited?
Further recommended reading; "Paul and the Hope of Glory" - https://www.amazon.co.uk/dp/B085XNC5QS?psc=1 . It's not about post-millennialism, which gets a tiny mention at the very end. As I'm trying to say, that is the point.