It's a challenge talking about this topic. It's very easy to come off as "I'm better than you" or "you are a bad person". But these conversations
can be productive and non-offensive.
I encourage people to see a wide continuum between eating 100% meat and eating 0% animal products. I express that I understand the challenges in decreasing one's meat consumption. I point out that it's not all or nothing - you can be "mostly vegan" (while still consuming animal products sometimes).
It's best to have conversations like this when the person is asking, not because you "caught" them eating an animal product.
Because of how grim the reality is for animals raised for food, most people are reluctant to be exposed to what it means. They will hope that (and not look for evidence against their belief that) the meat they buy comes from a better place (it's worth pointing out that in the US about 99% of meat comes from factory farms).
As I said - people's values are likely aligned. Polls consistently show that people do not approve of animal abuse.
The final argument that made me drastically decrease my meat consumption was the empirical fact that individual choices matter:while supermarkets are not 100% responsive (buying 1 item less decreases their next order by 1 item), they are responsive to demand. And if they buy in batches (which they likely do), you have a chance of triggering a "next-larger" batch order. On average it all works out to an (economic) elasticity of less than 1, but a far cry from 0 (depends on type of meat, but rough figure of 0.5 is a sensible underestimate).