I think this is the essence of it. “Poetry is the best words in the best order”. To write a good poem you not only have to choose the right word to express what you mean to say in the way you mean to say it, you also have to choose the right word to fit your metre and rhyme scheme. Even for gifted poets, this means a lot of going back and revising and even restructuring whole verses so that each word can pull double duty.
The good news is that humans have been composing poetry for longer than they’ve been doing almost anything else, and when people spend a long time doing difficult things they develop lots of techniques to do it. Techniques that anyone can learn - if they put in the time and effort. Geisel broke off his Oxford D Phil in English Literature but he clearly had the training in poetic techniques. There’s a good discussion here of the different metres he employed, and the rigour with which he stuck to them:
Some books by Geisel that are written mainly in anapestic tetrameter also contain many lines written in amphibrachic tetrameter, such as these from If I Ran the Circus:
"All ready to put up the tents for my circus.
I think I will call it the Circus McGurkus.
“And NOW comes an act of Enormous Enormance!
No former performer’s performed this performance!”
Geisel also wrote verse in trochaic tetrameter, an arrangement of a strong beat followed by a weak beat, with four units per line (for example, the title of One Fish Two Fish Red Fish Blue Fish). The formula for trochaic meter permits the final weak position in the line to be omitted, which facilitates the construction of rhymes.
Geisel generally maintained trochaic meter only for brief passages, and for longer stretches typically mixed it with iambic tetrameter, which consists of a weak beat followed by a strong, and is generally considered easier to write. Thus, for example, the magicians in Bartholomew and the Oobleck make their first appearance chanting in trochees (thus resembling the witches of Shakespeare’s Macbeth):
“Shuffle, duffle, muzzle, muff”
then switch to iambs for the oobleck spell:
“Go make the Oobleck tumble down
On every street, in every town!”
I think a big part of the answer as to why the rest of us find this difficult is that we haven’t spent any time doing disciplined study of and thinking about trochees, iambs, stresses, beats, etc. and without that technical grounding we’re at a major disadvantage.
ETA - another disadvantage of people not having that formal training in poetics is that when a company hires an ad agency to write an advert in teh form a poem, many people have to approve it and none of them can spot the error. I mean, you’d think they would, but that “Listen, if I can be civilised…” line was signed off by a lot of people and… none of them could count beats and stresses, apparently.