I think you should focus on your attitude. I think the best attitude is one of love and compassion, to be with the other people instead of against them.
I you are both very occupied in an argument neither of you will get anywhere because you are both too obsessed with telling the other one what he/she is doing wrong.
Vegetarianism and veganism have benefits for personal health, animal well being and environmental sustainability.
I have learned that veganism is an inevitable aspect of the human being when they become more spiritually awakened. Spiritiual awakening means developing more and more love towards life of any other being, human, animal, plant, etcetera.
Personally I have noticed an improvement of my well being as a result of a plant based diet. Feeling better makes it easier to be more compassionate towards other people and other life in general.
I have to admit that when I started to feel these improvements I wanted to tell everybody else about it. It's kind of logical: if something good happens to you you want to share it with others. But others may think differently and you have to respect that.
I want others to respect my way of living too.
Don't force yourself into anything that doesn't fit you or that demands too much from you. Won't work.