How and why does 'val' and 'case' affect the type system? (Especially the variance)

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Welcome to Scala version 2.8.1.final (Java HotSpot(TM) 64-Bit Server VM, Java 1.6.0_22).
Type in expressions to have them evaluated.
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scala> class E[-A]
defined class E

scala> class F[-A](val f: E[A] => Unit)
<console>:6: error: contravariant type A occurs in covariant position in type => (E[A]) => Unit of value f
class F[-A](val f: E[A] => Unit)
                       ^  
scala> case class C[-A](f: E[A] => Unit)
<console>:6: error: contravariant type A occurs in covariant position in type => (E[A]) => Unit of value f
   case class C[-A](f: E[A] => Unit)

scala> class F[-A](f: E[A] => Unit)    
defined class F

```