Writing directly benefits students' reading skills. For example, if you have students write about what they've read or learned (for nearly any content or age), you'll dramatically improve reading comprehension. Students are often forced to reread and think more deeply about what they've read.
There are, of course, a lot of good reasons why someone should learn to write. Many jobs require it — and often jobs that require a lot of writing pay better (though I’m sure many nurses would disagree with that last point). Of course, writing is also an important form of self-expression. Just as there are people who play musical instruments, dance, sing, paint, knit, cook, and so on, there are many who use writing as a form of self-expression, and a form particularly useful for preserving memory. All of those are terrific reasons for teaching writing.
Read more about the benefits of writing here: