The claim here is that humans can eat meat, and therefore it is ok to do so
The fact that your body can do something, or even that it's physically geared towards doing something, doesn't mean that it should. For instance, if you are a virile lad of good strength, you possess all the tools you need to sexually assault someone. That doesn't mean that you should be "omnivorous" regarding consensual and non-consensual sex, just because you can. Also, although I've never tried it, I hear that heroin feels amazing. Should you do heroin now because your neurons are geared towards flooding your brain with neurotransmitters when you take it? This is an absurd argument.
Just because something 1. feels good or 2. is within your physical capacity makes it neither a good idea nor morally permissible.
This is an equivocation on the term "Omnivore" When people talk about us being omnivores, what they really mean is that we are opportunistic omnivores, i.e. that we can survive off of meat if times get tough as we are running across the savanna. This condition of living on the edge of survival somehow includes putting frozen TV dinners in your shopping cart for eating every day, because they take "omnivore" to mean that you should eat a helping of meat at every meal. But The human body has evolved to help us survive starvation conditions, not for couch-surfing. Hence, it should be no surprise when this "omnivorous" lifestyle catches up with people.
People love to use "we evolved X to eat meat", but that doesn't work either