I believe the first 4-6 weeks of a new eating lifestyle (not diet) are the worst.
You don't have great momentum yet, there are a lot of firsts and new situations to handle, not to mention food, planning, exercise, etc.
And to add insult to injury, in these first several weeks you're not seeing a lot of easy victories, major milestones, etc. There are no, You look great!, Wow, what are you doing? comments that make your day.
It's easy to get discouraged and quit, and I think that's why many people do just that.
So why do some people throw in the towel and others forge on? It's probably different for everyone, but my 2 cents is you have to want it more than anything. You desire, your drive to change has to superceede everything in your life.
I'm convinced that if you can just push past those difficult challenges in the early weeks, you can make it happen.