A friend of mine asked if she could read one of my stories some day... every time she mentions it, I had brushed the thought aside. She's a "new" friend who works at the local library and has a European background and a literary taste similar to mine.
As writers, we gather friends around us who are other writers, readers, or "bookless" folk. When one of the more "bookless" friends asks to read something, I always worry it's just a polite offer to show interest in something I do. I avoid dealing with these offers. Until they get wrapped up in my literary pursuits some other way.
Now, writer friends fall into two camps: the anxious and the reluctant. Both are dangerous. The anxious writer friend wants to read you as soon as possible, as if to judge you and base your friendship on what your words do. These writers can be dangerous. They're the ones that can sometimes push too far in "helping" and try to influence your work in ways you don't want and then you're stuck telling them their ideas suck.
The reluctant reader is the writer friend whose voice you respect, and you want to read their stuff because you like them so much (becoming the anxious reader from above) and you want to know if they like your stuff. Almost like seeking compatibility as much as moral support. But you don't want to ask or be pushy.
My new friend is a reader, and readers are the best friends writers can have. They read the work and react to it without trying to influence it. They are honest without looking for things to fix and they can read the work without pushing their own style on it.
But as a friend, considerate writers need to remember not to overwhelm their reader friends with too many requests. That's why I'm often reluctant to take advantage of a new reader friend, because that level of intimacy changes the relationship. As the author, you have certain questions you want to ask, but you don't want to become a pest or desperate.
So, if you ask to read my stuff, remember this.