Part of it was psychological on the part of Henry. He seemed to view the lack of an heir from his spouse as a divine indictment upon he union. While I'm hesitant to give him a diagnosis from the distance of so many years, he did seem to exhibit a lot of signs of religion megalomania, and so to legitimize the illicit son wouldn't make as much sense as dissolving the union he felt was displeasing to God.

The other part ties in with his very real obsession over Anne Boylen and her refusal to be his mistress the way her sister had been. As he wanted her and wasn't used to having his wishes thwarted, the only option was legal marriage so he quite literally changed the world in order to make it happen.

So long story short it was a mixture of circumstances and his personality. There also isn't a precedent in English monarchy for a legitimized bastard inheriting the throne, and as the memory of the Wars of the Roses was still very fresh it isn't fair to just laugh off his obsessive need for an heir either. The Tudors were a new, barely legitimate line and Henry knew without a solid succession there would be another crisis.