Its kinda embarrassing, but I have no idea how all this rythm stuff works in music. I mean I get the basics of the notation, but I don't understand the idea of dividing music into small chunks. That is to say that to me you could do away with the time signature numerology and bar lines in sheet music and it'd be all the same. And indeed you can make music like that, notably Satie composed music in "free time"[1].
These days I realize that my experience is atypical and many (most?) have some sort of intuitive feel for this thing, it's not just me being dumb for not understanding fancy music theory but that my experience/perception of music is different.
When I was tutoring music theory, some students who had a similar experience had "aha" moments when we tried to focus more on how the harmony of a piece of music is linked to the meter.
So I wonder, how much do you hear harmonic changes in a given piece of music? Maybe a better way, for you, to develop an ear for rhythm is to focus on the regularity of those harmonic movements, which are what really "suggest" a meter in the first place. In most music, rhythm really is just the subdivisions of those larger "beats" implied by the harmony, and discussions like the OP end up being more or less "Oh, this is interesting because it doesn't line up with the expectations that accompany rest of the surrounding music"
You are right, I'm not very good with harmonic changes either, or functional harmony in general.
> it doesn't line up with the expectations
This idea of expectations comes up often when up when discussing music, and I get the impression that that people have stronger expectations than I do.
This whole situation leads funnily enough me happily listening all sorts of "complicated" music (jazz/prog/classical/electronica), not because I appreciate the complexity in any intellectual way, but because it just sounds fun. That of course doesn't help me reinforce any music pattern parts of my brain if I listen music that intentionally breaks all the conventions and "rules"
We listen to music with a lot of unconscious preconceived notions depending on our upbringing. Our brains enjoy grouping, repetition, structure. Also tension in the form of expectations and surprises. We can make music in free time without these patterns but to most of us it sounds less 'normal'. It's like if we make music with pitches in between the 12 notes of western tradition.
A lot of those preconceptions are to do with the stresses in a bar/measure. Things like when drums are hit or when melodies begin and progress. Misusing this leads to the same effect as stressing the wrong syllables in speech. Something like a waltz (which is 3/4) depends on stresses in a pattern of 3 beats, matching the dance. If you write a waltz as the same notes in 4/4 the patterns that should align on 3rd notes will not relate to the written form. Stresses are also why 3/4 and 6/8 are distinct - they are identical in values but the grouping of notes is not. They can also differ because the actual rhythm as played can differ from how it is written i.e. swing.
If you imagine the melody along with 'twinkle twinkle little star' and stop, it should feel unresolved because of the note it ends on. You need 'how I wonder what you are' to feel comfortable again. These two phrases should have a relation and similar grouping. It's harder to notice but within each of these phrases there's a pair of bars that have a similar relation.
For straight-timed pop music, think about it like the markings on a ruler. Everything is based on a doubling or halving of something else.
Pick some reference event, like how your foot would want to tap along with the song. If you listen, something in that song (perhaps the snare drum) occurs twice as frequently. Doubling again, perhaps the hi-hat. In the other direction, halving the frequency of your foot-tap might coincide with a chord change. Halving the chord changes may reveal repetitive patterns in the lyrics. Eventually big chunks of the song (verse/chorus/solo) reveal themselves to start on some 2^n number of toe taps.
My favorite example of this is "Your Love" by The Outfield. If you play it alongside an incrementing counter in binary[1], you can see how certain instruments/elements align with changes in one of the bit positions. When large runs of bits roll over to zero, that tends to coincide with important structural points in the song.
These days I realize that my experience is atypical and many (most?) have some sort of intuitive feel for this thing, it's not just me being dumb for not understanding fancy music theory but that my experience/perception of music is different.
[1] https://en.wikipedia.org/wiki/Free_time_(music)