Songwriting is not a skill, it's a talent. It is certainly a talent than can be improved upon - after 3 1/2 decades of writing for a living, I still try to write better songs, and I believe I improve constantly. But a certain amount of talent is a prerequisite to being any good at it.
Though I can see his point of view, I disagree with Roger...
I think songwriting is both a skill & talent...
And both can be improved upon...
By writing...
But each of us have our own approach to the craft...
And hopefully we are having fun!
Scott mentioned the FAWM challenge...
There is also the 50/90 challenge
http://fiftyninety.fawmers.org/I urge you to go there & listen to some of the songs...
Some are crap & some sound great (ear of the hearer I guess

)...
The drawback for me is finding time to listen to the songs of others & make fairly quality comments...
While still trying to concentrate on writing.
Here it is easier to listen & comment because there are far fewer submissions...
Well... there use to be

!