It took me a long time to stop eating meat, longer than I would have liked, but I managed to stop when it finally felt like I wasn't going without - and that's a lot of work for someone raised in meat and taters.
But one thing I do know is that shaming people or making people feel bad for eating meat isn't the best way to go about converting people to vegetarians... It just makes you look like a jerk.
If you want to help people eat less meat, provide easy recipes for full meals that have a meat like substitute that doesn't suck. What worked for me was beans - specifically black bean burgers because I love burgers - so it took a long time to find the right black bean burger for me.
It just takes starting with one thing - and if it ends with one thing, that's okay too because that person will consume less meat because of the change.
People also need to be eased Into it. The stop eating meat approach doesn't work but if you give me a good ass recipe to try and it just happens to not have meat Its not that big of a deal and nobody feels like they're being converted.
I eat meat but being Mexican I also have plenty of recipes and meals that are vegetarian in nature. Enchiladas de queso fresco, tostadas de frijoles, sopes vegetarianos, caldo de garbanzo, esquites, calabasa y elote a la crema, quesadillas. Just to name a few off of the top of my head. That's not even counting stuff like cereal, pancakes, etc. All of them are vegetarian and delicious and non were pushed on me for vegetarian reasons, they're just a part of my culture. I have tried to make a small effort to eat a bit less meat for health reasons but I don't think I'll stop. If we approached the issue in another way we might get more people to just eat less meat and it's a step in the right direction.
My fiancee is half salvadoreña and half Lebanese and when I told her she already eats a significant percentage of vegetarian meals she didn't believe me until I went through her last weeks meals. Baby steps people, small baby hamster steps.
There is also the problem that a lot of times the argument for why it's better is not framed properly. Plenty Of Studies have shown that if literally everyone were to suddenly go vegetarian we would have the exact same problem just now with vegetables instead of meat. The supply wouldn't be there things would get ramped up emissions and resource use especially water would increase drastically to try and keep up with the demand.
If you're going vegetarian just because you don't like the idea of eating animals then that's fine, but if you're at all coming at it from the sustainability perspective then the true solution is a dietary mix that is more heavy towards the vegetarian side of things but still with some meat mixed in just not a dietary staple eating constantly.