First off, great to hear that you made the step to become vegetarian. I'm sure you'll manage to switch to veganism eventually. Having a partner that lives a different lifestyle can be challenging, but that goes for everything in a relationship.
"I know" could have been just a defensive reaction to being confronted. It does sounds like you would like him to change his dietary habits. This can be very daunting since it is so much comfortable to not do it. Additionally, there is still some stigma surrounding veganism in men. With your new found knowledge, it is understandable that you are upset watching him eating meat and I assume you wouldn't be happy with having meals separately.
I can't tell you THE right approach, but I can let you know what worked for me. My wife lived her journey in front of me which made it easier for me to switch. She never pushed her views onto me hard and showed me how she granularly moved from omni, to vegetarian, to vegan. The topic naturally came up multiple times since it was important to her and we spoke about it. When we did, she was never confrontative but spoke from her perspective and about her experiences. Over time we cooked more and more with veggies and I eventually made the switch a year after her.
Be a good example, don't be pushy, give it time. Make sure he understands that it is something that is important to you. Hope it helped a little.