I actually think this is a legitimate concern. Here's my rationalization: Plants probably don't have a sense of individuality. Personally, I wouldn't care about eating parts of an animal that grew back (like eggs or milk). Plants seem to be no different.
I don't think it's clear why the root of a plant like a carrot should have any special significance except to us. What about onions, turnips, potatoes, etc?
I meant a carrot is something that would probably be more individualized than say a strawberry. So I get your point about eating from plants that grow back, but I guess a carrot wouldn’t fall under that categorization.
Also, what about animals that regrow limbs? Would you eat the arms of a starfish every so often?
I think it's possible combined with ethical farming practices I could be convinced it's not so bad to eat starfish arms (although they don't sound very appetizing).
To be clear I do already eat meat today. I am just not convinced about its necessity and am interested in ways to avoid doing it.