The irony of subjectivity
Subjectivity is technically ironic, because to "be objective" seems perfectly obvious. However, Hegel has such a low opinion of human "objectivity," that he basically lumps all human belief and opinion into the "subjective" box, saying that no matter how sure a human is of their own opinion, their opinion is too limited to be trusted, and there is the problem of contrary opinions and the influence of culture. Humans are ironically unfit for philosophizing about the nature of reality.
The irony of suffering and death
The problem of suffering and death is ironic, in Hegel's estimation, because these problems drive history forward. Progress is oriented around suffering reduction, and the history of medicine, for instance, seems oriented around staving off death, and yet—somewhat ironically—all living beings on earth live and die. The problem is central to human history, and the diversity and beauty of culture seems inextricably linked to the hugeness of these problems.
Religion and its ironies
Religion is ironic for many reasons. Firstly, religious opinion is diverse, but also similar. All religions have human life and death as their central question, and they all deal with human suffering. Even Eastern mystic philosophies have patterns of belief for dealing with these obvious problems. Religion is ironic because it is focused on both dogma and progress, and it is also ironic because it seems to be the most important philosophical consideration of all, but there is simply no scientific way to sort through the issues.
The irony of linear time
Time seems to be self-explanatory, but it really isn't. One might say that Hegel's entire philosophy is a response to the strange "a priori" or linear time. There is no denying that things change through time, and time seems to be consistent, but though it is observable, it is philosophically impossible to explain. There is no rational explanation for what time is or why it happens, and Hegel's appreciation of history begins with this ironic conundrum.
The irony of empiricism
Empirical observation is when a person subjects their opinion to what is available through their senses. The approach can be thought of as scientific, instead of religious, but ironically, though Hegel writes in defense of empiricism, he notices that when viewing the entire history of humanity, empiricism is a faulty approach, because to be empirical would be to assume that everyone was being honest about their subjective points of view, so by observing other human testimonies, one sacrifices their philosophical ability to be "objective." One must admit that their point of view is so limited that it doesn't matter for much on this large a scale.
