The comments responding to you are pretty unnecessarily hostile, but I personally get where you're coming from. I personally think it's best to watch the thing so that you can be best informed, even if it's hard to do. Not even because of veganism being ethical, but because the fear of the unknown is a lot scarier than any documentary could be, IMO. Information is power, and having information (even distressing information) is empowerment.
Also, I loved meat too, but when I went vegan, I never really missed it. I was pretty worried about missing certain foods (one was sushi), but that never really happened to me.
I tried for a while to make those small changes, but I always found it too hard to do, until I finally just decided to cut out all animal products one night, and I never really went back.
I think the difference was how I framed it, mentally. I always saw it as an act of willpower to not eat animal products, like I have to overcome my cravings in the same way I would if I was cutting calories. But quitting animal products altogether allowed me to frame it differently for myself -- instead of telling myself "I shouldn't eat this", I can just say "I don't eat this." Like, it's not on the table as something I have to consider. I don't even have to recognize animal products as food.
Maybe if you cut things out one at a time you could do a similar thing. Though one problem is that it's a series of changes and commitments you have to make, instead of just one thing. I feel like that could be harder, depending on who you are.