Because these people do choose to include meat in their diet (seafood is muscle tissue from a live animal and therefore meat), they are not vegetarian as vegetarians do not consume meat.
Many vegetarians consider them to be cheaters for eating the flesh of an animal, and get rather offended when pescetarians call themselves vegetarians.
The main reason they get offended is that vegetarians and vegans alike believe that no animal should be consumed by humans, and if flesh is consumed, they are no longer worthy to the grand title of vegan or vegetarian. Another reason they are appalled is the conditions of the animals that are commercially raised and sent to be processed in the slaughterhouse.
Pescetarians believe that catching and eating fish in the wild is perfectly okay. They believe it to be humane, sustainable, healthy, and overall very delicious. Fish are always preyed on by other bigger fish, who either chomp them alive and eat them, or swallow them whole. Pescetarians are saving fish from that fate, as well as getting a good source of healthy calories, protein, zinc, omega 3 fatty acids, thiamin, vitamins B6 and B12, riboflavin, selenium, and other essentials the human body needs to stay alive and fit.
"No, thank you I'm a pescetarian. I'll have the lime-marinaded grilled salmon with a side of steamed rice and garlic-sauteed portobello mushrooms.
Bob: I saw you eat fish the other day, you are a pescetarian.
Lauren: lulz wat is ay pesctatariann!!111!!!!
Bob: A vegetarian that also eats fish.
Lauren: I am a pescetarian, then :3
No I think she is a pescetarian now that they have moved in together....how about sushi?