So some species proactively go about hunting, while others passively graze always remaining on the look out so that they can evade predators. For a variety of reasons (such as difference in diets as well as differences in evolutionary pressures) hunters have substantially larger/more advanced brains than prey have

You present this as a dichotomy. Are chimpanzees hunters? Well, you wouldn't say that it is their primary mode of subsistence but they do occasionally hunt. Are dolphins hunters? Well they have to catch prey so that would make them hunters. Is hunting what makes these species have relatively large and/or complex brains? To some degree, I'm sure, but isn't it more likely related to their sophisticated communication, co-operation, and group dynamic? Lots of species are hunters but not many species demonstrate a level of intelligence that chimpanzees and dolphins do when it comes to group dynamics (for lack of a better word, my terminology escapes me at this moment and primatology was never my area of specialisation).

we are the dominant species on this planet

But dominant in terms of what? We're not the most numerous species and we're probably not the most wide-spread or resilient (don't forget that 70% of the earth's surface is water).

Humans are the MOST adaptable species

Good luck finding me a citation for that. Once you hit graduate studies, you'll see why I bring you up on that statement. You could write a college textbook on what adaptation is and how it can be quantified. In what ways are we the most adaptable? Do you mean a tendency to evolve adaptations or that in our current form we are able to live in a diverse geographic range and operate in a large number of unique niches? If the latter is including artificial influences (e.g. clothing, housing), it doesn't really speak to our fundamental biology and physiology but rather the point can be more succinctly put as "humans are more intelligent than any other species".

We are also the MOST successful at whatever it is that we decide to do

Can we dive to 2,500m below sea-level? Maybe with the help of technology but I seriously doubt we'd be the most successful organism at that depth. Can we fly? Sure, but again I doubt we'd be the most successful organism in the air at that time. You have an incredibly anthropocentric view of evolution and biology. Humans can do a lot of things as we're not particularly specialised as a species but that also means we're probably not going to be the best at whatever speciality we practice.

Dominating our environment and our ability to get into "wars" stem from the same underlying trait in humans, and it is a trait that many other species have

Is this a biological trait? I guess It must be if other species have it. When did we obtain this trait? Was it before anatomically modern humans left Africa or was it after? Because we certainly weren't dominating our environment at that time and warfare was a long way of yet.

We naturally want to compete with eachother

Have you heard of natural selection? Every organism competes with one another. More commonly its intra-species competition. It may not involve violence (as I stated before) but it is competition. If every organism didn't compete with one another, then they would never have evolved via natural selection.

effectively compete with any environment in the planet

When you say environment, are you talking about an ecosystem or the physical environment itself (weather, geography, geology, etc)? Because we certainly weren't competing with every and any ecosystem thousands of years ago (or even now for that matter). If you're talking about the latter then I'm not sure what you mean since we don't compete with rocks and weather for anything.

We always come out on top

I'm going to assume you're talking about ecosystems because humans will never 'come out on top' against the environment. The environment will always win because if we kill it, it will kill us. If you're talking about ecosystems, try living at 2,500m below sea level and get back to me.

all the higher more advanced species have an element of competition within themselves

Haha! OK, it makes sense you studied at an undergraduate level but really they should've dispelled this idea in that limited time you had in these classes. What the fuck is a 'higher, more advanced species'? Evolutionary theory and thought has come a long way in the last 150 years, catch up would you?

when you deal with higher organisms

facepalm

These are competitions with no apparent "physical value", because the competition only exists because we "made it up"

What do you mean by no physical value? Are you saying that these competitions have no bearing on an individual's survival or reproductive success? Because that's ridiculous. That would cast aside the entire subfield of sociobiology. Hell, it can even go the other way where our cultural practices and behaviour influences our biological evolution.

but many other creatures share this same trait because of the same evolutionary reasons.

Share what trait?

In its simplest, rawest form, this "competition" between us is war.

What? Playing sports is not war, playing a game is not war. You say yourself that these competitions have no physical value but then you speak of this competition as war? How is it war? You seem to think that conflict or competition is synonymous with war; it is not.

I really don't follow your train of thought. On the one hand you talk of competition between individuals and species but then on the other hand you go on to say that this competition has no physical value and is expressed as activities like sports and games. How are sports and games a competition in your sense of the word?

created this trait

I'm really going to need you to explain this 'trait'.

Humans need to compete with each other, and war is an inevitable byproduct of that once you factor in the complexities of society.

You mean humans need to socially compete with each other (not biologically)? So sports leads to war? Funnily enough, some forms of warfare in the Pacific/Melanesia are more analogous to what we would consider sports than warfare. In one area, when the British arrived they even managed to replace this native form of warfare with the sport cricket. The cricket games served the exact same social purpose as the wars did.

Your theory touches far more on cultural evolution than biological evolution. Biological evolution is the bigger picture, it gave us the ability to form cultures and societies, but it is the advances in our culture and societies that leads to warfare (judging by what you've said, and I'd largely agree with this too). The thing is there is no decent evidence of warfare prior to about 10,000 BC. It might not even go that far back as the evidence is still highly contentious and it's pretty hard to say definitively one way or the other. It's not until you hit about 5,000 BC that the ball really gets rolling.

And I apologize for coming off as a jerk at first

I didn't really notice. Apologies for the long reply, no need to reply to my points if you have better things to do. I'd rather be clear the first time than have to repeat my points.

I hope you realize I am not/was not claiming to know more than I really do

I can understand but your reply to me above comes across as if everything you say is true, or at least widely accepted. Really, it is not. About the only true thing you said was that evolutionary biology is not as easy as people think (particularly people on the internet who've read the Origin of Species and think they know all they need to about evolution). You will learn (if you continue your studies) that you can rarely expect to be right about anything you say. Your writing will eventually reflect this (as I hope it has mine) and you will shy away from stating definitives and instead make statements based on probabilities and a weighing of evidence. It's a good practice to follow because it means you are always evaluating your stance and are less liable to confirmation bias.

Your views on evolution will change the more you study. I may have written something similar to you after my first course on evolution at university. I tend to find a book or an article that 'humbles' me every now and then in the sense that it puts me back in my place, it makes me realise evolution isn't so straight forward and not everything can be modelled or predicted. It's important to find such works every now and then because you can easily get carried away when you don't test your convictions frequently. I've found that reading Stephen Jay Gould and G.C. Williams are great in this respect.