As your teacher's question to you was originally worded it assumed that this Brecht poem is satire. Let's look for a moment at the definition and an explanation of satire.
the use of humor, irony, exaggeration, or ridicule to expose and criticize people’s stupidity or vices, particularly in the context of contemporary politics and other topical issues. (Oxford Dictionaries, online)
The purpose of satire is to ridicule a person, social convention, group of people, or practice.
Ridicule can be mild such as that used by Oscar Wilde in his very humorus play, The Importance of Being Ernest, which also heavily employs irony and exaggeration.
The tools of satire employed to achieve ridicule are humor, caustic wit, exaggeration, sarcasm, and/or irony (one or more may be used, though more than one is often employed).
Ridicule can be stronger such as in the caustic, sarcastic ridicule of Jonathan Swift's "A Modest Proposal," which uses sarcasm and extraordinary exaggeration to make a caustic point about poverty in Ireland during British rule.
The mild form of humorous satire is called Horatian while the stronger form of caustic satire is called Juvenalian.
The question is, does Brecht's poem display the characteristics of satire?
The premise of the poem is meant to be understood as depending on significant irony. Written in the first half of the 1900s, during a time when "reading history" was an enterprise left to academics in "ivory towers," the title alerts the reader right away to the irony: workers did not have the leisure, the education, the background or the opportunity to read history during most of Brecht's life time (1898-1956), yet here is a worker reading history. All the questions the worker/reader poses indicate that he does not understand history the way academics understand it, which is another irony. The worker/reader understands history from the laborer's perspective upward while the academic understands history from the perspective of the elite (new social and cultural historians also look from the elite downward to the laboring populace).
There is irony but is there humor, wit, or exaggeration? I see no humor nor any exaggeration: all is straightforward facts followed by straightforward questions:
Phillip of Spain wept as his fleet
was sunk and destroyed. Were there no other tears?
One might say there is wit since it is deliberately very suggestive questions that follow the statements. Specifically, the questions suggest the unrecognized lives of the myriad individuals who (willingly or unwillingly) do the work of the great ones whose names are remembered;
... And even in Atlantis of the legend
The night the seas rushed in,
The drowning men still bellowed for their slaves.
Is something being subjected to ridicule? The definition of ridicule is:
the subjection of someone or something to contemptuous and dismissive language or behavior (Oxford Dictionaries)
Based on the definiton of "ridicule," it is not possible to say there is any ridicule as there is no contemptuous or dismissive language in this poem. The poetic persona's voice is that of a sincere, though questioning, worker, not one of a ridiculing observer of the worker/reader.
So do we have satire or not? We have irony. We have no ridicule. We have no humor nor any exaggeration.
Satire: Satire is a literary form through which a writer pokes fun at those aspects of society (Martha Tolleson, Collin College).
While Brecht, a political and philosophical Marxist, ironically points out the neglected legions of unpoken human history, he is doing it from the perspective of sincere inquirey and sincere objection: he is not poking fun at an aspect of society he disapproves of; we have no ridicule. Thus the verdict of analysis seems to be that we have no satire.
Yet, if you must see this as satire, and if irony alone may fulfill the requirements of satire, then we may say that this is satire because Brecht ironically brings into examination the extreme contradiction between life as it is and has been lived and how life is recorded and immortalized. Thus it is satire because an historically insignificant worker is reading hisory and asking historically significant questions that important academics failed to ask about important aspects of reality.