A couple years into being homeschooled myself my mom implemented a journal. I was required to write a page per day of something, it didn't matter what. I remember agonizing over it at times. A whole page of what?! It was certainly some form of torture she'd concocted, I was sure of it.
Despite my childhood disgruntlement, I followed in my mother's footsteps when I began requiring my son to write in a journal starting in 1st grade. He's now in 2nd grade and is finishing up this, his first journal. When he initially started writing in it, it was a real struggle. He is a perfectionist, so when there was a misspelled word it was difficult, when he couldn't think of what to write there were often tears. There have been many times where I've listed off a couple of topics that he could write about so as to circumvent despair.
We're not all cut from the same cloth and certainly there are people who will never particularly enjoy writing. I'm sure some of this has to do with exposure, though. The less exposed you are to something, the less likely you are to pursue it.
In the course of my son's writing experience we've really tried to make it enjoyable. I don't over correct his grammar or his spelling - that will come in time. I do for the most part make sure his punctuation is correct. I feel like he's old enough for that now. I try to stress that it's more about creativity than having everything perfect.
He has acquired a pen pal who he's never met, which is exciting for him. He has written several stories that have had zero requirements specified from me. He has written a couple reports. In addition he has written comic strips, thank you notes, and he is currently writing a play script. If you think I'm bragging, then you're right. I'm extraordinarily proud of him.
I'm really thankful that my mom prescribed writing as a daily activity. It certainly fostered a love of writing in me. I've had personal diaries since the age of nine. At this point, I have lost count of how many I've had. I just know that writing for me has been more than just an assignment, it has been an expedition. I am beyond thrilled that my son is now embarking on his own.