What's the part of a song called that people get obsessed with called?

It's often, but not always, the chorus.

i've always heard it referred to as the hook ...

I think the part of the song you hum is the riff. The hook involves lyrics.

Definitely not the lyric. How many poems have you come across that have a hook? The lyric can and should play a part but only where it augments and highlights the rhythmic and tonal or melodic components. Just listen to this Steve Winwood song and note how the hook is established in the first bars and it's 30 seconds before any words arrive (and notice how they augment the hook)



Here's another particularly delightful example that demonstrates how rhythm and tonality/melody create the platform that hooks our attention and then how the words are in the service of the patterns already established. It isn't that the words are not important but rather that they serve the greater good and in this case how they serve it very well indeed



PS... my family has instructions to play only this video at my funeral

This really depends on the structure of the tune. Consider a 12 bar blues — you think about the whole tune because it comes back around every 12 bars. And while most blues compositions have a similar harmonic structure, what's memorable, for me at least, is how the tune resolves in measures 9 - 12. If it's done cleverly, it can become the "hook".

A typical 32 bar tune might have two 8 bar sections that form the first 16 bars, which are then repeated, which is called A-B-A-B, or it might be constructed with four 8 measure sections, commonly referred to as A-A-B-A. The 8 measure B section is called the "bridge". Thelonious Monk said the the bridge is what makes the rest of the tune sound good.

This Miles Davis tune is in the A-B-A-B form (with a short piano intro):


In this Monk tune you see the A-A-B-A form with the bridge:


But not all tunes are 12 or 32 measures long, and there are A-B-A-C and A-B-C-D forms and 24, 36, 48, and 54 measure tunes. Cole Porter's "Begin the Beguine" is 108 measures long!

In any of these tunes, you're likely to be humming the whole structure, not just one part. In fact, I can't think of a "song" where you wouldn't hum the whole tune unless it's one with a specific introduction, like Sonny Rollins has here, Intro-A-B-A-C:


Then there are interludes, special endings, shout choruses, and verses — which are often played or sung at a slower tempo or even in a different key. "Stardust" has a 16 bar verse followed by a "refrain":


And then, composers can write tunes any way they wish and are not confined to any particular form if they have something to say and want to push the envelope. So, to sum up, pop tunes are composed of memorable "melodies" which can be constructed and modified in all sorts of ways, but if I find myself humming a particular tune I'll probably take it through the whole form because that lets me follow the melody from beginning to end and resolves any harmonic tensions — and that's usually what makes a tune moving and memorable.

You ain't no slouch.

This is an instrumental from Eminem's "So Bad":



This is the part of the song I think about and hum.

This is the part of the song that had gotten stuck in my head.

The hook of a song is often referred to as the lyrical part that gets repeated over and over.

What part of the song are people more obsessed with- the instrumental or the hook?

Is the instrumental the same thing as the beat?

According to https://www.quora.com/Whats-the-difference-between-a-chorus-a-refrain-and-a-hook:
The hook simply means any part of the song that draws the listener’s attention (and get ingrained in the listener’s memory) the most.

Can't an instrumental be a hook, as in this case?