Eh, op is right and wrong. You certainly can get everything you need and be very healthy as a vegan, but... if you eat about what a normal person eats except without the meat and cheese? you are, as they say, gonna have a bad time.
As a child, I insisted on being a vegitarian - as long as my parents cooked for me (and were careful to see to it that I had a balanced diet, compete proteins, lots of nutritional yeast, etc... They had spent time as vegetarians themselves, so knew how to do that.) I was quite healthy.
After I moved out? I did very poorly, because I wasn't willing or able to put in the effort to see to it that I had balanced nutrition.
That's the thing; as a meat eater? There are a lot of ways for me to get complete nutrition (and yes, it comes with a lot of other things that I don't need, but at least I get what I do need.) - so even someone who puts minimal effort into eating a balanced diet is not going to suffer from deficiencies very often, if they eat meat in the traditional manner. (Quite the opposite, really.) If you put the same effort in but avoid all meat and animal products? at least in the place and time where I live? You are probably going to make yourself sick.
In a culture where most people eat meat, you need to put in a lot more effort and research in order to avoid deficiencies as a vegetarian.
You could argue that this is a truism and that the same could be said for a meat-eater in a culture that just ate vegetables. Most cultures have evolved a traditional set of foods that won't leave you with severe deficiencies of anything, and so if you cut out certain classes of food from that tradition, you need to pay more attention to what you are consuming in order to see to it that you get enough of the nutrients you need.