It took me a long time, many years, to become fully vegan, and I still cheat for good butter. And I eat honey and I wear leather shoes.
I started on the journey after reading Diet For A Small Planet -- my mother had a copy kicking around -- and was completely appalled that they were razing forests in Argentina to grow beef for McDonald's hamburgers.
I quit eating meat, though I still ate cheese and eggs. Once every few months I'd got out for a hamburger with everything, and for a while I continued eating fish at family gatherings. It was probably years before I gave that up. And I only stopped eating eggs because I figured out they were giving me a rash, and cheese because it didn't agree with me either.
Unfortunately, "sustainably" grown beef actually isn't, despite industry claims to the contrary: it still requires large quantities of water as well as grazing acreage that can feed only a fraction of the planetary population. Grazing cows still fart methane. It's more humane for the cows, and if the cows aren't fed hormones and antibiotics, it is healthier -- but it's not sustainable for everyone to continue eating current first-world quantities of meat.
And the amount of meat we eat today is historically unprecedented: here's a graph from the World Cancer Research Fund, which wants you to cut back on eating meat because it's statistically linked with more cases of cancer. Correlation isn't causation, of course, but the data keep piling up
Chicken and eggs, by the way, require a lot less in the way of resources than red meat. Fish is pretty problematic given the violence to ocean environments of industrial-scale fishing operations.
Changing to a more sustainable diet doesn't have to be all-or-nothing. When I was a kid growing up in northern New Hampshire, billboards everywhere proclaimed, "Wednesday is Prince Spaghetti Day." These days, many families aim for Meatless Mondays or Vegan Wednesdays (or "Vednesdays," if you like your alliteration). Some families go vegetarian during the week but not on weekends. We cook vegetarian and vegan meals at home, but one member of the family chooses to eat meat at restaurants.
You can make a great vegan sauce for spaghetti or lasange by replacing the meat with chick peas, navy beans, tempeh, or bits of fried tofu. If you add a little parmesan for flavor, that's still healthier for you AND the planet than feeding half a pound of ground beef to everyone at the table.
If you want to drift toward vegetarian or even vegan, it doesn't have to mean a commitment to self-deprived asceticism. You can start by adding one recipe to your repertoire. A couple of weeks later, try out another. Make sure you find foods you LIKE. Instead of thinking in terms of cutting out meat, think in terms of adding vegetarian or vegan meals, or parts of meals, to the rotation, and spacing out meat-heavy meals. Maybe you'll continue to change over time; maybe you'll find a point where you're comfortable.
But the data are clear: reducing meat consumption, and in particular beef and dairy products, is the most efficient way to reduce your own carbon and water footprint. Eliminating beef from your diet would have more impact than giving up your car.