In my professor's words, "Apollo walked into Mt. Olympus like a man wielding a nuclear warhead, and Zeus, always with the coup of his father on his mind, was worried that his powerful son would upset the balance of Olympus and claim leadership as head of the gods."
Certainly Apollo was considered a powerful god, but much of the contemporary sources I've read have been in reference to his divinatory and musical qualities. I'll admit that the theme of a god whose genealogy is rife with fathers killing sons being afraid of his son is poetic. But are there sources that support this claim that Apollo was somehow a threat to Zeus genuine?
There is a tendency among educators to try to simplify Greek mythology into a central narrative, where the gods have a fixed story with fixed relationships.
The relationship between the gods differs from region to region, era to era, and author to author. You're likely to find Apollo to be more prominent, say in Delos or Delphi than Olympia.
To answer your question more directly, the Homeric poet describes Apollo and Poseidon serving the Trojans as punishment for attempting rebellion against Zeus in Iliad XXI.
Also, according to Hesiod's Theogony, (886-900) Metis was prophesied to bear a son more powerful than his father. The prophesy leads Zeus to swallow her, eventually giving birth to Athena through his skull. This isn't anxiety about Apollo specifically, but against being overthrown.
You might also see the Homeric Hymn to Apollo, where Apollo returns in triumph and the gods "tremble before him" (τρομέω) and his mother Leto disarms him as he enters the House of Zeus. This might imply that she prevents conflict between them.
Iliad, Homer
Theogony, Hesiod
Homeric Hymn to Apollo, Homer
Challenges to the Power of Zeus in Early Greek Poetry, Noriko Yasumura
Not THAT related to the question, but what is the difference between the god Apollo, and the titan Helios. Is there one? If there is one, why did the greeks worship 2 sun gods, even tho they had only one in the sky?
I am not a historian but I am a fan of the Theogony. I cannot support the part about Zeus controlling Apollo, but some texts do portray Zeus as being worried about a son overthrowing him like he overthrew his father Cronos.
The passage I have in mind concerns him swallowing his first wife, Metis, before she could give birth to children more powerful than him:
Theogony (886-900): "Now Zeus, king of the gods, made Metis his wife first, and she was wisest among gods and mortal men. But when she was about to bring forth the goddess bright-eyed Athene, Zeus craftily deceived her with cunning words and put her in his own belly, as Earth and starry Heaven advised. For they advised him so, to the end that no other should hold royal sway over the eternal gods in place of Zeus; for very wise children were destined to be born of her, first the maiden bright-eyed Tritogeneia, equal to her father in strength and in wise understanding; but afterwards she was to bear a son of overbearing spirit, king of gods and men. But Zeus put her into his own belly first, that the goddess might devise for him both good and evil."
You can find the full text of the Theogony here
End of Book 8 of the Iliad would suggest he's wrong:
Zeus' badass boast of his power
Come, try me, immortals, so all of you can learn. Hang a great golden cable down from the heavens lay hold of it, all you gods, all goddesses too: you can never drag me down from sky to earth, not Zeus, the highest, mightiest king of kings, not even if you worked yourselves to death. But whenever I'd set my mind to drag you up, in deadly earnest, I'd hoist you all with ease, you and the earth, you and the sea, all together, then loop that golden cable round a horn of Olympus, bind it fast and leave the whole world dangling in mid-air— that is how far I tower over the gods, I tower over men.
I am not a classicist and this is just a partial answer, but this is how one of my professors explained it to me.
In Hesiod's Theogony, Zeus fights the serpent Typhon for control of the cosmos after the war with the Titans. He defeats the serpent and casts it down into the abyss of Tatarus and then proceeds to rule over creation as the new king of the gods.
Now Apollo wasn't around at the time of the war with the titans and was only born later. After he is born he begins wandering the Earth and in his travels he meets and defeats the serpent Python. Python is an even older and greater beast than Typhon, suggesting that the author of the Hymn to Apollo was taking a jab at those who worshipped Zeus by suggesting that his god was even more powerful than theirs (who was supposedly the greatest of the gods).
Sources:
Hesiod's Theogony
The Homeric Hymn to Apollo
It doesn't directly relate to the mythology, but thematically, Apollo often represents order and reason, and the "Age of Apollo" is seen as a step towards modernity away from the more chaotic and visceral age of Zeus. Each generation of the Greek mythology can be seen as an abstraction further away from chaos towards order.
Some of the responses here highlight an important fact - conceptualizations of the gods change over time. It is also worth noting Zeus' fear of a son, as explained in the Theogony. All of that said, Apollo was not the son in this prophecy. One resource I haven't seen anyone quote is Homer's Iliad, which is explicit in stating that Zeus is the most powerful of all. Here is an excerpt from Book 8: "[1] Now Dawn the saffron-robed was spreading over the face of all the earth, and Zeus that hurleth the thunderbolt made a gathering of the gods upon the topmost peak of many-ridged Olympus, and himself addressed their gathering; and all the gods gave ear: [5] “Hearken unto me, all ye gods and goddesses, that I may speak what the heart in my breast biddeth me. Let not any goddess nor yet any god essay this thing, to thwart my word, but do ye all alike assent thereto, that with all speed I may bring these deeds to pass. [10] Whomsoever I shall mark minded apart from the gods to go and bear aid either to Trojans or Danaans, smitten in no seemly wise shall he come back to Olympus, or I shall take and hurl him into murky Tartarus, [15] far, far away, where is the deepest gulf beneath the earth, the gates whereof are of iron and the threshold of bronze, as far beneath Hades as heaven is above earth: then shall ye know how far the mightiest am I of all gods. Nay, come, make trial, ye gods, that ye all may know. Make ye fast from heaven a chain of gold, [20] and lay ye hold thereof, all ye gods and all goddesses; yet could ye not drag to earth from out of heaven Zeus the counsellor most high, not though ye laboured sore. But whenso I were minded to draw of a ready heart, then with earth itself should I draw you and with sea withal; [25] and the rope should I thereafter bind about a peak of Olympus and all those things should hang in space. By so much am I above gods and above men.” So spake he, and they all became hushed in silence, marvelling at his words; for full masterfully did he address their gathering." (trans. A.T. Murray)
But yes, the best course of action would be to attend office hours.
Question: there is a theory that Apollo was formerly Aplu, the Hittite/Hurian god of plague (hence the association with healing). Is that widely believed, and if so would there have been a region in Asia Minor where both Zeus and Apollo were known, but with Apollo "on top" as the locally known god?
I wonder if your professor was trying to emphasize Zeus' particular capacity for making allies of potential rivals in general using Apollo as an example, rather than implying that Apollo is a natural suspect for usurpation?
Apollo's power tends to evoke a sense of neat-and-tidy rational capacities that keeps him mostly in sync with Zeus' will, not opposed to it.
As to Apollo being "more powerful" than Zeus, I wonder if this was meant in some special sense? Zeus is pretty big news when it comes to raw power. The "Golden Cord" speech Zeus gives at the beginning of Book 8 of the Iliad is a beautiful description of Zeus' power in his own words.
The following isn't exactly a classical writing, so I'll understand if the moderators don't allow it, but the dynamic you're describing does appear in the song "To Anacreon In Heaven", the anthem of the 18th-century Anacreontic Society and the song that "The Star Spangled Banner" was based on. The full text of the song contains Apollo directly intervening to save the Anacreontic Society from Zeus' wrath, implying that he had the power to stop Zeus' thunder:
Apollo rose up, and said, "Pry'thee ne'er quarrel,
"Good King of the Gods, with my Vot'ries below:
"Your Thunder is useless" — then shewing his Laurel,
Cry'd "Sic evitabile fulmen^1, you know!
"Then over each head
"My Laurels I'll spread;
"So my Sons from your Crackers no Mischief shall dread,
"Whilst snug in their Club-Room, they jovially twine
"The Myrtle of Venus with Bacchus's Vine."
1 - Latin for "this repels thunderbolts"