What other people eat doesn't bother me much if at all any more, perhaps it used to -- it's not my business. And I know that some animals are carnivores, etc. Even being vegetarian isn't harmless, people point out that worms and mice and so on are killed when a field is used for agriculture.
Some people try to be fruitarian because of concerns like that -- I think of that (semi-extreme food discipline) as being more like what Jains do than Buddhists.
Since you're interested, the Christians have doctrine on the subject -- Matthew 15 which Christians read as exempting them from Judaic dietary laws:
Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man.
Do not ye yet understand, that whatsoever entereth in at the mouth goeth into the belly, and is cast out into the draught? But those things which proceed out of the mouth come forth from the heart; and they defile the man. For out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies; These are the things which defile a man; but to eat with unwashed hands defileth not a man.
I don't know an equivalent doctrine in Buddhism but so far as I know it's similar or identical.
How to handle the scenario below or how to answer them to make them comfort/understand base on Buddhism or logic.
If someone asks me "why?", I just say, "Oh, lots of reasons."
If someone asks again I might, "Well I reckon it can be good for your health, good for the planet, I find the treatment of farm animals horrific, and so on."
But I'm not trying to push my view.
It can be inconvenient for the cook though.
Note that I think Buddhist monks aren't always able to be vegetarian I think the vinaya requires them to be "easy to support" (not to be picky/demanding eaters).
The tough part is when my partner is inviting me to Christ, they will pray for thankfulness for the food.
Maybe they can be thankful for their food, whether or not it's also your food.
Don't forget, they are all civilised, very civilised.
Any guide for this specific topic?
I've heard or had the lobster argument. I imagine other people have too, though if they're young perhaps there's always a first time. I don't know that this kind of argument is ever effective/beneficial/persuasive though I guess it is sometimes.
After the lobster is chosen and cooked might not be the most effective time to discuss it, a better time might be when you're shopping or planning a meal.
To some extent this is samsara (birth and death), to which apparently the proper attitude is nibbida.
See also SN 7.2 which is ostensibly about food but more particularly about not participating in someone else's argument.
My parents had a not very-well-trained dog when I was small, I learned not to get between him and his food especially -- at meal-time I'd fill and drop his food bowl for him and get my hand out of the way, to avoid being growled and snapped at.
Likewise what I remember of people's reactions or facial expression, if I tried to disparage, argue against or take away their food at the table, was that it wasn't really very welcome!