I'm glad you asked that question. The simple fact is, I'm not that original a musician.
Something I'd like to point out, however, is that there are thousands of musicians who don't write their own stuff. They're called "classical" and "jazz" musicians. No one goes up to Nigel Kennedy and says "Hey, I like all that stuff you do but how come you don't write your own violin concertos?". Or "Hey, Art Tatum, nice piano standards but how come you don't write your own stuff?"
But, somehow, if you have an interest in popular music and especially if you play guitar, people immediately assume you're a singer-songwriter or something.
To me there's SO MUCH good music out there to be learned (and so much mediocre original music to be shunned) that it takes all my time just trying to figure out what the creative geniuses have done.
It's true that with some musicians this study of previous masters has lead to their own ability to find a compositional "voice" and begin to write. I don't think I was born with that gene, frankly. (Gene Frankly...I think I went to college with a guy by that name)
But, all that being said, I am interested in writing. I do *occasionally* get the inspiration. I've got a handful of ideas right now that I'm kicking around, but they never come out to much and I can't seem to develop them beyond the 30 seconds or so of what interests me about them. And then I get tired of hearing them.