Why are arrays covariant but generics are invariant?

The reason is that every array knows its element type during runtime, while generic collection doesn't because of type erasure.

For example:

String[] strings = new String[2];
Object[] objects = strings;  // valid, String[] is Object[]
objects[0] = 12; // error, would cause java.lang.ArrayStoreException: java.lang.Integer during runtime

If this was allowed with generic collections:

List<String> strings = new ArrayList<String>();
List<Object> objects = strings;  // let's say it is valid
objects.add(12);  // invalid, Integer should not be put into List<String> but there is no information during runtime to catch this

But this would cause problems later when someone would try to access the list:

String first = strings.get(0); // would cause ClassCastException, trying to assign 12 to String

Via wikipedia:

Early versions of Java and C# did not include generics (a.k.a. parametric polymorphism).

In such a setting, making arrays invariant rules out useful polymorphic programs. For example, consider writing a function to shuffle an array, or a function that tests two arrays for equality using the Object.equals method on the elements. The implementation does not depend on the exact type of element stored in the array, so it should be possible to write a single function that works on all types of arrays. It is easy to implement functions of type

boolean equalArrays (Object[] a1, Object[] a2);
void shuffleArray(Object[] a);

However, if array types were treated as invariant, it would only be possible to call these functions on an array of exactly the type Object[]. One could not, for example, shuffle an array of strings.

Therefore, both Java and C# treat array types covariantly. For instance, in C# string[] is a subtype of object[], and in Java String[] is a subtype of Object[].

This answers the question "Why are arrays covariant?", or more accurately, "Why were arrays made covariant at the time?"

When generics were introduced, they were purposefully not made covariant for reasons pointed out in this answer by Jon Skeet:

No, a List<Dog> is not a List<Animal>. Consider what you can do with a List<Animal> - you can add any animal to it... including a cat. Now, can you logically add a cat to a litter of puppies? Absolutely not.

// Illegal code - because otherwise life would be Bad
List<Dog> dogs = new List<Dog>();
List<Animal> animals = dogs; // Awooga awooga
animals.add(new Cat());
Dog dog = dogs.get(0); // This should be safe, right?

Suddenly you have a very confused cat.

The original motivation for making arrays covariant described in the wikipedia article didn't apply to generics because wildcards made the expression of covariance (and contravariance) possible, for example:

boolean equalLists(List<?> l1, List<?> l2);
void shuffleList(List<?> l);