The only creature that can form a concept of importance is humans; so humans are the only ones able to make a scale which can measure importance. It’s like Toyota choosing the criteria for car of the year.
Uh-huh.
I, for one, am sick of being a Toyota in this universe of… oh. Wait. There aren’t any other makers. Just a few zillion different bicycles and skateboards.
But what if we’re the skateboards and something else is the car? Personally, I’ve always held the tapeworm in very high regard - but I won’t go into that now.
The only argument in favor of the superiority of humans is that we get to define what “superior” means. 
Not counting that we *can *define what superior means. Along with several million words in thousands of languages.
So yeah, that’s true, but I think that’s kind of the winner: we are, quite literally, the undisputed champions, because nobody else is bothering to dispute it with us.
No other species much cares about this trophy we’re giving ourselves, which is fine. The meaning we have in our lives is the meaning we construct in our lives, and if we want to hold a “Species Most Likely To Succeed” vote and then cast all the votes for ourselves, cool, we’ve just given ourselves some meaning.
That said, if we were so inclined, we could certainly come up with another standard for the blue ribbon in the species contest:
-Highest population
-Most biomass
-Longest continuous survival of species in current form
-Lowest levels of intraspecies violence
None of these are tricks that humans can currently accomplish with our technology.
And if our descendants are around, they will be filled with bacteria, just as we are now.
Yeah, things like importance and centrality and meaning and significance and obligation and value aren’t ultimately a matter of science or logic, but of philosophy and/or religion, or something simpler and more arbitrary like intuition or “because we say so.”
Well, there’s the one that left the planet to plant its flag on the moon.
Even if that is true (and I don’t accept that it is), it still does not follow that we are the “dominant” species.
Most of the prey animals, I’d wager… keep an eye out when you’re at the watering hole, if something moves, freeze and maybe it won’t see you, but if it charges, run like hell and hope it eats somebody slower.
So to move this within the human sphere, the largest family of the oldest, fattest, and most timid individuals would ‘win’?
Robot bacteria. Humans aren’t going to be biological in 500 years, let alone 4 billion.
Win what?
If you’re realizing that there’s no prize for that, you’ll also realize that owners of magician shops aren’t winners in the real world either. Indeed the only blue ribbons available for anyone are the ones made by ribbon manufacturers; they’re not just lying around to be discovered.
In other words, whatever definition of dominance you come up with is one you came up with, which is precisely the point.
From the context of the rest of your post, you don’t appear to actually be claiming this, but it’s not even a credible argumentative premise. All of the available evidence is that life is not unique to earth. That evidence being the nature of the evolutionary process and the number of stars and galaxies and probable number of habitable planets in the observable universe – and incidentally also the observation that chemistry and physics, the precursors to biology, work the same way everywhere in the universe.
So while it’s mathematically possible that earth is the only planet in the entire universe that harbors life, science doesn’t usually spend much time on hypotheses that are literally astronomically improbable.
The only reason we’re not being overrun by extraterrestrials – most of whom would likely be a good deal smarter than we are if you consider the incredibly short span of time in which we’ve even existed, let alone possessed technology – is that the universe seems to possess an interesting balance in which its plethora of life exists in an incredible vastness enforced by relativistic limitations on travel and communication. Plus, we are probably about as interesting to advanced civilizations as an ant farm. 
No, we have that obligation because we invented tools and, in our awesome superiority, proceeded to use them to destroy the environment and everything in it. We are the only species that doesn’t live in harmony with nature, but that isn’t a necessary result of possessing technology, it’s a result of possessing primitive technology – things that consume resources that aren’t replaceable, and produce long-lasting byproducts that harm the plants and animals in the environment including ourselves. It is technology in a transition stage, still fundamentally that of the 18th century industrial revolution.
Anthropocentric and anthropocentricity seem like the right words. Basically a sort of collective ego. It seems to take two different forms, both having their original expressions in the inventive teachings of religions.
One is that we are unique in the universe, specially created and looked after by the Big Guy. In this concept the rest of the universe is basically for decoration in the night sky. The other is that we are unique on this earth, distinctly special and different from all other animals. Since it’s undeniable that we have annoyingly similar traits to many such animals, it was then posited – again by religions – that the difference is defined by our unique possession of a Soul, which is conveniently both undetectable and undefinable.
Humans’ competitive advantage is the collective transgenerational capacity to develop, store and transmit knowledge and skills through culture, within which human importance is a pivotal postulate.
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Humans are entitled to be anthropocentric.
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Anthropocentrism is humans’ belief that humans are the most significant beings around and from many perspectives they can be regarded as central.
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“The most significant beings around” is a justified label because homo sapiens is virtually safe against natural enemies.
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Human centrism is a justified position due to the level and complexity of what humans can achieve.
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Human assessment is a valid and functional tool; one can’t use it in certain fields and discard it in others.
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There is no such thing as an unbiased assessor; misanthropists may be even more prejudiced than human exceptionalists.
Thus, it’s only natural that one should be anthropocentric.
“I don’t see any reason why not” is not evidence however.
Your argument falls at the first hurdle as this is a meaningless statement.
For the other points, note that for the purpose of this thread, we’re talking about whether a particular belief or behaviour is fallacious, or in other words, irrational.
It’s irrelevant what caused a particular behaviour to exist, or if there is anything stopping us thinking a certain way. The beliefs that the OP discussed e.g. assuming everything was crafted for humans, are clearly fallacious (even if the assertion is later found to be correct, the reasoning is flawed).
I’ll rephrase it: “Humans are entitled to anthropocentrism.”
Is it still meaningless in your opinion?
It may be so, but despite everything I think I’m doing no harm if I point out anthropocentrism is still justified.
Who says you can’t have it both ways? There’s not necessarily anything mutually exclusive about the idea of a vast universe that operates on a scale incomprehensible to human beings, and there existing a God that knows and values every little intelligent lifeform.
If NdGT’s Cosmos has a singular thesis thus far, it’s that, as vast and empty and hostile and alien as the universe may be, it’s the littlest events on the smallest scale, like a chance meeting between 17th century academics, or an asteroid being deflected a single meter to the right billions of years ago, or a renowned author and scientist taking time out of his day to show some kindness to an aspiring teenage astronomer, that can produce the most significant and wonderful things.