The primary motivation behind this shuffling of scenes was to create a more balanced, linear narrative. As pointed out by Jackson himself, including Shelob in The Two Towers would give Frodo and Sam little to do in The Return of the King other than toss the Ring and wait for the eagles.
Furthermore, Tolkien's The Two Towers is set out so the first half deals with the Rohan storyline, while the second half charts the journey of Frodo, Sam and Gollum. This format doesn't work for a blockbuster movie, and Jackson weaves the two narratives in the style of a conventional film. However, this risked confusing viewers since the timelines don't always match up.
If Jackson had adhered to the book ending, Sam would discover Frodo was still alive at the end of The Two Towers, then Gandalf and Pippin would arrive in Gondor during The Return of the King's first act. In the story's chronology, however, Gandalf rocking up to Minas Tirith on Shadowfax happens before Frodo is captured by orcs. Consequently, it made sense to include the Shelob material at the beginning of the third movie to ensure a simpler narrative structure and give Frodo and Sam a proper arc before finally reaching Mount Doom.
A second possible reason for the changes concern The Two Towers' climax. The Helm's Deep battle provides Peter Jackson's The Two Towers movie with a stunning conclusion that's hard to top. The audience would be so exhausted from this epic Lord of the Rings clash that adding Shelob onto the end would potentially feel like a tacked-on epilogue in a movie context. Using Helm's Deep as the final battle and ending on the cliffhanger of Gollum's betrayal created a more traditional film structure and ensured the Shelob fight could be afforded more prominence in The Return of the King.