Many people- mostly students, ask themselves this question on a daily basis. Whether it be because they have a paper due in their one o'clock class and they haven't started yet or because they just got back what they thought was a solid English midterm and ended up with a C+ on the essay portion. So why should we write?
For one, it builds character and professionalism if you constantly seek to make yourself both more literate and intelligent in the use of vocabulary and overall diction. Everybody is going to need to know how to craft a comprehensive and impressive resume some day so that they can apply for the job that they want. Writing for pleasure and for other purposes can all improve your overall ability, similar to speaking a foreign language.
Another reason that you should take every opportunity to write is because it will help you to grow your own vocabulary over time and even writing for academia versus writing for fun or for your job can have intrinsic value as well. Not only will it help to chronicle important events in your life and to keep one memory and adventure distinguishable from another some day, but writing out your very thoughts could spur a creative storm that pushes you towards new endeavors or energetic projects.
Don't be discouraged when you receive feedback or criticism for your writing, whether it be comments and critiques from your professors or letters back and denied offers from publishers. The greatest authors among us even struggled to get published and no matter how good their works were they were all turned down at some point. If Stephen King had given up on his first few attempts to get published then we wouldn't have the amazing and dark stories that we do today, and that's just one such example. Take constructive and even the destructive criticism you may receive and extract whatever value you can from it before moving on.
The most important reason of all however is one that you may not expect. You should write because you want to, not because you are required to during school and may as well continue to practice afterwards. You should write because something within you enjoys being able to pen words that describe what you are thinking and visualizing. Writing was created as a method of communication that could transcend boundaries that word of mouth could not. Writing is no feeble communicative tool but rather the full might of evolution put to work.
At times, I will admit it is tough to find the drive to write articles or to churn out essays and presentations. Sometimes you hit a mental wall and are unable to progress past the impediment. However, as it has become a necessary skill in modern business and synonymous at times with success, writing is a must so it is imperative that you find a small niche that you enjoy.
Every time you write something down you are imparting a small bit of your thought and soul into it. Whether you are writing eloquent poetry or arguing the philosophical qualifications for veganism, it speaks to people of your own stance as well as how you view our world. Enjoy your own creativity and don't get discouraged when it is difficult to summon.