Since you asked why C# did it this way, it's best to ask the C# creators. Anders Hejlsberg, the lead architect for C#, answered why they chose not to go with virtual by default (as in Java) in an interview, pertinent snippets are below.
Keep in mind that Java has virtual by default with the final keyword to mark a method as non-virtual. Still two concepts to learn, but many folks do not know about the final keyword or don't use proactively. C# forces one to use virtual and new/override to consciously make those decisions.
There are several reasons. One is performance. We can observe that as people write code in Java, they forget to mark their methods final. Therefore, those methods are virtual. Because they're virtual, they don't perform as well. There's just performance overhead associated with being a virtual method. That's one issue.
A more important issue is versioning. There are two schools of thought about virtual methods. The academic school of thought says, "Everything should be virtual, because I might want to override it someday." The pragmatic school of thought, which comes from building real applications that run in the real world, says, "We've got to be real careful about what we make virtual."
When we make something virtual in a platform, we're making an awful lot of promises about how it evolves in the future. For a non-virtual method, we promise that when you call this method, x and y will happen. When we publish a virtual method in an API, we not only promise that when you call this method, x and y will happen. We also promise that when you override this method, we will call it in this particular sequence with regard to these other ones and the state will be in this and that invariant.
Every time you say virtual in an API, you are creating a call back hook. As an OS or API framework designer, you've got to be real careful about that. You don't want users overriding and hooking at any arbitrary point in an API, because you cannot necessarily make those promises. And people may not fully understand the promises they are making when they make something virtual.
The interview has more discussion about how developers think about class inheritance design, and how that led to their decision.