Writing large buggy programs is hard. To say a program is buggy is to imply that it is at least of sufficient quality to approximate what it’s supposed to do much of the time. For example, you wouldn’t say that Notepad is a buggy web browser. A program has got to display web pages at least occasionally to be called a buggy browser.
Writing large correct programs is much harder. It’s even impossible, depending on what you mean by “large” and “correct.” No large program is completely bug-free, but some large programs have a very small probability of failure. The best programmers can think of a dozen ways to solve any problem, and they choose the way they believe has the best chance of being implemented correctly. Or they choose the way that is most likely to make an error obvious if it does occur. They know that software needs to be tested and they design their software to make it easier to test.
If you ask an amateur whether their program is correct, they are likely to be offended. They’ll tell you that of course it’s correct because they were careful when they wrote it. If you ask a professional the same question, they may tell you that their program probably has bugs, but then go on to tell you how they’ve tested it and what logging facilities are in place to help debug errors when they show up later.