We can't even seem to treat each-other decently. Animals have no chance.
If you didn't, why not?
Here's a more detailed breakdown for you: http://www.adaptt.org/killcounter.html
Also, is there a definition of 'level of cognition' that you can give which encompasses fish, rats, birds, etc. (everything on the link you provided), and does not include ants?
https://www.vegansociety.com/go-vegan/definition-veganism
The key is - "as far as is possible and practicable". It's entirely reasonable and quite easy to adhere to a plant-based diet, whereas avoiding stepping on ants is an impractical goal which detracts actual steps you could do to reduce harm.
Of course, there's no reason for veganism and your concern for ants to be mutually exclusive. Take Jain monks as an example.
> Jain monks and nuns represent the ideal of Jainism. These men and women try to separate themselves from the everyday world. They are not allowed to kill any living creature. They carry brooms to sweep all surfaces to avoid crushing insects accidentally. Monks may not own any property except a broom, simple robes, bowls for food, and walking sticks.
I would say that humanization is a prerequisite for treating anything humanely (and the inverse is true as well, see: dehumanization). IMO, the primary reason animals do not have a chance is because they are not universally (or sufficiently) humanized. This could be in large part due to our grossly insufficient or oversimplified understanding rather than intentional malice.
The fact that we don't treat actual humans humanely is an orthogonal issue.
Ultimately, it may not be that things that are sentient have inviolable rights; it may be that we simply draw a moral circle around ourselves and if you're close enough in the circle, you're protected; if not, you're not. There may be a good historical reason for that; there's anthropological evidence that our early ancestors shared the planet with creatures who were a lot closer to them in both look and behavior than anything living today and that were competing fiercely and in a zero-sum style for overlapping resources. It's not a large leap to imagine that our developed morality therefore accounts for creatures with every bit the cognitive capacity of your own that you cannot coexist peaceably with for risk that they'll end you and your entire bloodline by out-competing you.
Whether that's the way we should approach the world (in a modern era where our species dominates the planet's resource allocation and is threatened by functionally zero complex organisms) is a reasonable question; it may very well still be a framework that describes morality for a great deal of the planet's population.
So there's not much point to saying we should treat animals humanely by driving humans extinct.