Read the article I linked. It's a respectable piece of reporting, not some hack work. If you believe any of the named, on-the-record sources in it, Obama does a lot of his own writing. His make-or-break race speech after the Revered Wright explosion, for example, was almost entirely him. Favreau's work was dropped, and he was relegated to typing what the candidate said and doing some line-edits.
There are plenty of legitimate places to ding Obama, but to go at him about writing is borderline insane. He's one of the very few politicians to have actually written his own books, and all reports from within his campaign and admin suggest that he does much more of his own writing than any president in the last thirty years.
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