so im trying to answer this question for my music teacher and i'm trying to do research of it, but she hasn't been very specific with the question...any help?
This question brings to mind the line...
How far do you want to take this question about why rather than how or when?
If animals aren't compelled to do something for their survival, they tend to rest. Actually, rest is part of survival, because it doesn't waste energy. Rest is a state to seek out to maximize survival.
Fast forward through to a bunch of metaphors about music, physical mechanics like up/down, simplicity equals stability, etc. and get to the idea that a tonal center is a place of rest.
Symbolically people like arriving at that point of rest, because rest is an ideal state to be in.
That little chain of idea is my own, but it's similar to a common textbook description which equates tonal center with home. It's a general notion of rest, safety, familiarity.
Why do you think many people are drawn to a tonal center?
I'm not sure I buy into the whole idea that strongly.
Sure, there are dynamics in music about center, balance, regularity, etc. But I don't think "tonal center" is so important compared to rhythm. A lot of music just alternates auxillary tones around something I would call a reciting tone. I suppose that could be a "tonal center", but that seems too sophisticated a term for such simple music. Schoenberg called that kind of simple music "primitive." So, I sort of reject the basic premise that a tonal center matters to many people.
This has been a big question for centuries. It's more in the realm of psychology than music. One place to start is David Butler's article: "Describing the Perception of Tonality in Music: A Critique of the Tonal Hierarchy Theory and a Proposal for a Theory of Intervallic Rivalry" which is available on JSTOR. One can sometimes get JSTOR access as an individual. Students can get access through their institution.There are other works going back to Helmholz and Seashore (and even Plato).
Some, though by no means all, sounds in nature are periodic looked at from the time domain, consisting (very simplistically) of a set of harmonic partials, each a multiple of a fundamental frequency, when looked at from the frequency domain. There is an evolutionary advantage in being able to identify such sounds and perceive their pitch and timbre: You can tell if the cry of an animal is close or far away; or if it's a small or large animal, for example. As a human, being able to distinguish pitch and timbre is a useful social tool that helps distinguish voices, and later on in the evolutionary timeline, gives the ability for spoken language to evolve, which gives another survival advantage.
To this end, our auditory system has evolved to become very good at recognising harmonic series, and reconciling them into the perception of a certain pitch and timbre.
Following on from that, you can create an interesting and stimulating aural effect - you might even see it as an illusion - by playing periodic sounds together that are related in pitch by a simple ratio, such as 2:1 or 3:2. The ear to can to some degree recognise these as different sounds - after all, they each have their own harmonic series present. But some of the partials of the notes will be the same - for example, if we play notes of 100 and 150 Hz together, we'll get partials at 300, 600, 900... (and so on) Hz that are in common to both notes. This causes the ear to simultaneously also want to hear them as the 'same' sound, because they do also have that common set of partials.
What we could do, if we wanted to be really interesting, is to start with one note, and then add a couple more notes that had a simple frequency relationship with those, and then perhaps add in a couple more notes that, in turn, had a simple frequency relationship with those...
...and that's what tonal music is, essentially - the creation of a hierarchy of frequency relationships around a particular note, that the ear will naturally hear as the 'centre' of the whole set of patterns because it is the focal point of the way the patterns of shared harmonics fall together.
As humans have evolved, we've developed not only perceptive abilities, but we also develop cultural preferences. It's likely that some cultures would become particularly interested in the aforementioned interesting aural illusion of related frequencies, and some would become interested in other aspects of sound. And that does in fact seem to have been the case - we have cultures that have developed a lot more complexity in rhythm, we have cultures that have become interested in inharmonic, bell-like sounds, and ended up with different sets of pitch ratios relating in different scales, but we also have cultures that have become interested in exploring the complexities of frequency relationships between sounds whose timbre follows the harmonic series. This inevitably leads you to the concept of a 'root' note or pitch in some form, because the ear is forever trying to see if it can reconcile the patterns of energy it's detecting at different frequencies.
A thought experiment
In a sense, there's no hope of finding the right answer to this question until you can show the equivalence of all the various tonal systems present in human music—and even then, what if we discover aliens whose scales and modes are just like those used in Western classical music, except that the aliens regard the locrian mode as the most stable and beautiful and couldn't possibly fathom ending a song on a major triad? The fact that the scales and modes are the same would lend evidence to the Pythagorean theory of frequences related by integer ratios; the fact that a diminished chord is chosen as the tonic would lend evidence to the constructivist notion that tonality is just a product of cultural training.
In the absence of forbidden nature/nurture experiments in search of a universal grammar of tonality, it's important to consider what tonality really means. Many people will tell you that tonality means establishing a certain pitch as the tonal "center," and then creating tension and release by moving (harmonically) "away from" and "toward" the center. Every conventionally tonal piece starts in a "stable" place, moves to an "unstable" place, and then returns to "stability," if you view it from a sufficiently broad vantage.
But notice that all this talk of "centers" and "stability" has nothing to do with what's literally happening when we play music. D♭ and C are close together in frequency but relatively unrelated harmonically, but vice-versa for G and C. You can argue that G and C are "close" because their frequencies are in near integer ratios, but what's so special about integers? Why aren't irrational frequency ratios considered more beautiful expressions of human life, because they create a composite wave that varies endlessly instead of repeating? But let's suppose that integer ratios are, normatively, better—then how do you explain the many musical contexts in which a transition from a D♭ to a C chord does sound great and convey a sense of arrival? How do you explain extratonal practices like blue notes, bending, and detuning that make music sound more warm and accessible, despite the math?
Tonality is a metaphor
The notion of a tonal center is not a formula from which we derive the rest of music theory. It is a metaphor that helps musicians conceptualize what they are playing and composing. Musicians know what they mean when they speak of being "far" from the tonic, even as they recognize the shortcomings of the metaphor.
So, I would turn your question around a bit:
Why do you think many people are drawn to a tonal center?
They are drawn to a tonal center because it a compelling metaphor for the mysterious phenomenon that is music.
But music is broad, and tonality is not the only metaphor available for understanding it. We can also develop a robust theory of tension and release surrounding rhythm, lyric, orchestration, or cultural context. I would encourage any music student to investigate these elements independently in order to gain a fuller picture of how they work together to make music exciting and resonant.