Computers do not hurt skills when it comes to grammar and spelling. The teacher or professor does not have to stress about spelling and grammar because the computer is helpful in that area. I believe it actually hurts people when they have to use long hand. Writing a long paper can be strenuous and in due time, your hand will give out. It can be a bother to type a long paper, but you do have the use of both hands and not one.
Most people choose to use a computer because it is very accessible.
When your mind has collected how you should begin your paper, all you have to do is apply yourself and begin typing. Also by using a computer, there is not a need to re-write your essay. That is why hand writing your five-page essay, these days, just does not make any sense at all. However sometimes we are forced to write by hand because we do not have an access to a computer at all times. Computers can also help you with other things than just writing.