Ok, but if my girlfriend leaves me, my dog doesn't think "poor guy, I know how that feels". Empathy is understanding other's feelings and being able to imagine yourself in his shoes.

I mean, they might get basics like "sad" or "excited" and instinctively copy them, but that's it.

But whatever, this is far removed from the point of the thread anyway.

So after your logic we should kill our self too, because the human species is probably the biggest parisite on the planet ? 

Sure there is always going to be a cognitive disadvantage which impedes how empathetic the dog can be, but this is not a binary of "has empathy"  vs. "does not have empathy." There are degrees of empathy. The cause of empathy in dogs is no different from the cause of empathy in humans. It is a mixture of chemical reactions induced by a combination of stimuli and cognitive processing. In the dog it is much more stimuli based, while in a human there exists empathy that is cognitive, but that doesn't mean there is not stimuli based empathy in humans and cognitive-based empathy in dogs. A lot of people will cry because they see somebody they love hurt without even understanding why they are hurt, for example. That is just as much empathy as understanding is. Empathy isn't just about understanding other people's emotions, but also about feeling other people's emotions. Sometimes it is necessary to understand one's emotions to feel them. Other times it is not. Dogs and Humans incorporate both. Humans being much more intelligent are capable of greater degrees of cognitive empathy, of course though. 

The definition of a parasite requires two (or more) living beings in a symbiosis from which one gains resources at the expense of the other. Humans usually have mutually beneficial relationships with most species we interact with. We eat cows, for example, but the cows have benefited from this domestication by higher population rates.  

Nevertheless, his argument assumes that people put higher value on human life than the life of other species. I think most people are humanists and agree with such a sentiment. That doesn't mean other species aren't valuable, just less valuable than humans from the perspective of humans. 

I very much so enjoy living. I largely enjoy the things we get to experience as human beings; 

The sad truth is we haven't done squat to better anything about this planet and have often times gone out of our way to disregard other species to make this world more enjoyable for us.  I just don't feel like it's right and that there might have been another path we could've taken early on in human history (it's nearly impossible at this point, but there's always hope).

I don't believe it was our destiny as a race to bring about the ultimate destruction of the only planet we've found that exhibits life. We live in a beautiful disaster

Anybody remember what happened when the wolves were all hunted in Yellowstone? Yup, shit got thrown outta balance. That's what will happen if you eradicate a species that is an integral part of something larger. Eradicating a species to make us more comfortable living our lives is a huge fuck you to mother nature. Unless of course that species is invasive and was introduced to a foreign ecosystem, in which case get it out of there if at all possible.
Viruses? Damn straight we should eradicate them. That is what I've been trying to say. Don't kill off the mosquito; make sure every human is prepared to fight off the disease they carry.

Could they even be called sentient beings?

One definetion of sentience is the ability to modify ones environment to increase one's survivability. This is why humans can live nearly everywhere on the planet.

See Kardashev Scale

question is: wiping them out for what reason? if they answer is to help the human population the next question would be: if the human population is constantly growing why should we do anything to increase the growth rate as long we are bound to this planet with limited resources?

I have no sympathy for bugs and lesser species to be honest. They don't function like us they don't think or feel so it's hard to care about them. If eradicating a species is the best option for human survival then I think it's ok.