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I mean, she looks more Latina than English.
Yeah, as others have pointed out, she's not saying she is a professor who is English, she's saying she's a professor who
teaches English. The line before this is "My thesis always sounds like it was written by a geriatric gibbon with an acute allergy to English." - so she responds to say it's lucky he ran into her, because English is literally her department. There are several other lines where she mentions being part of the English department (e.g., MC: "I always thought there was a rivalry between the English department and the library." / Veronica: "Psh. We create the art. They just store it for us.") and her bio/description in the MC's phone says: "English Professor at Hanford's. We started hooking up about six months ago."
None of these are instances where you would generally insert your nationality, even if it's not the same as the country you're in. If you're Chinese and you teach physics, you would say "I'm a physics professor", not "I'm a Chinese professor."
Plus, as was pointed out while I was typing this, she's presumably Chilean - Veronica: "Please. I was raised in a Chilean household. Chilean women invented the jealous Latina stereotype."