From your line of reasoning, I'd guess that you have no moral issues with eating humans. If eating animals and plants is the same, then isn't eating non-human and human animals the same?

If you do have a moral problem with eating humans, then you probably have moral hierarchy - humans' lives are the most important, and every other life is less important.

Some vegetarians have a different moral hierarchy - animals' lives are most important, then plants' lives. You can value plants' lives, and treat plants with respect, and still decide that you're morally okay with eating plants.