If you could override a var with a var, then the overriding member could have a narrower type. (That's how overriding is defined.)
You could then assign a value of a wider type and then read it expecting the narrower type, and fail.
Illustration of the setter involved:
scala> class A ; class B extends A
defined class A
defined class B
scala> abstract class C { var x: A } ; class D extends C { var x: B = _ }
<console>:13: error: class D needs to be abstract, since variable x in class C of type A is not defined
(Note that an abstract var requires a setter in addition to the getter)
abstract class C { var x: A } ; class D extends C { var x: B = _ }
^
scala> abstract class C { var x: A }
defined class C
scala> class D extends C { var x: B = _ ; def x_=(a: A) = ??? }
defined class D