Why can't an anonymous method be assigned to var?

Others have already pointed out that there are infinitely many possible delegate types that you could have meant; what is so special about Func that it deserves to be the default instead of Predicate or Action or any other possibility? And, for lambdas, why is it obvious that the intention is to choose the delegate form, rather than the expression tree form?

But we could say that Func is special, and that the inferred type of a lambda or anonymous method is Func of something. We'd still have all kinds of problems. What types would you like to be inferred for the following cases?

var x1 = (ref int y)=>123;

There is no Func<T> type that takes a ref anything.

var x2 = y=>123;

We don't know the type of the formal parameter, though we do know the return. (Or do we? Is the return int? long? short? byte?)

var x3 = (int y)=>null;

We don't know the return type, but it can't be void. The return type could be any reference type or any nullable value type.

var x4 = (int y)=>{ throw new Exception(); }

Again, we don't know the return type, and this time it can be void.

var x5 = (int y)=> q += y;

Is that intended to be a void-returning statement lambda or something that returns the value that was assigned to q? Both are legal; which should we choose?

Now, you might say, well, just don't support any of those features. Just support "normal" cases where the types can be worked out. That doesn't help. How does that make my life easier? If the feature works sometimes and fails sometimes then I still have to write the code to detect all of those failure situations and give a meaningful error message for each. We still have to specify all that behaviour, document it, write tests for it, and so on. This is a very expensive feature that saves the user maybe half a dozen keystrokes. We have better ways to add value to the language than spending a lot of time writing test cases for a feature that doesn't work half the time and doesn't provide hardly any benefit in cases where it does work.

The situation where it is actually useful is:

var xAnon = (int y)=>new { Y = y };

because there is no "speakable" type for that thing. But we have this problem all the time, and we just use method type inference to deduce the type:

Func<A, R> WorkItOut<A, R>(Func<A, R> f) { return f; }
...
var xAnon = WorkItOut((int y)=>new { Y = y });

and now method type inference works out what the func type is.

Only Eric Lippert knows for sure, but I think it's because the signature of the delegate type doesn't uniquely determine the type.

Consider your example:

var comparer = delegate(string value) { return value != "0"; };

Here are two possible inferences for what the var should be:

Predicate<string> comparer  = delegate(string value) { return value != "0"; };  // okay
Func<string, bool> comparer = delegate(string value) { return value != "0"; };  // also okay

Which one should the compiler infer? There's no good reason to choose one or the other. And although a Predicate<T> is functionally equivalent to a Func<T, bool>, they are still different types at the level of the .NET type system. The compiler therefore cannot unambiguously resolve the delegate type, and must fail the type inference.

Eric Lippert has an old post about it where he says

And in fact the C# 2.0 specification calls this out. Method group expressions and anonymous method expressions are typeless expressions in C# 2.0, and lambda expressions join them in C# 3.0. Therefore it is illegal for them to appear "naked" on the right hand side of an implicit declaration.