You could as easily ask why they needed the original Harrier developed in the 1960s. The justification back then was the (correct) belief that if the Warsaw Pact went to war with NATO then Nato's airfields would be amongst the first targets and any air asset that could be operated independently of big concrete runways after such an attack would be invaluable. In spite of the views of many of the light blue's top brass (who also spent most of the sixties deriding the Buccaneer, until they had no choice but to adopt it as their primary strike aircraft), the Harrier proved itself to be versatile, adaptable and in 1982 the only option for deployment to the warzone around the Falklands (all their Lightnings, Phantoms, Buccaneers and shiny new Tornados sat impotently on the sidelines).
The more far sighted members of the RAF realised that a strike platform that could go anywhere, even onto the decks of the Navy's carriers, meant they could potentially be involved in any future military operation and not get left on the sidelines. The Harrier made up a significant portion of the RAF's strike force until 2010, and by throwing in with the Navy on the subject of it's replacement they negated the usual inter service rivalry the Government normally relies on to screw everyone over when Defence Reviews come around. A common fleet shared between the two services meant lower purchasing and operating costs compared with buying two distinct types, and originally the F-35B was only supposed to replace the joint Harrier force.
Tornado was supposed to be replaced by the Future Offensive Air System, which was separate from the F-35B purchase, and was supposed to be a mix of manned aircraft and UCAVs. The F-35 in either A, B or C variants were contenders for the manned part of the project, though no choice was made and the project cancelled in 2005 (partly to pay for the Iraq war, along with four then six batch 2 Type 45 DDGs). The UCAV part of the project is alive and well (now called Future Combat Air System, FCAS), but without any other manned combat aircraft on the horizon the F-35B became the de facto replacement for the Tornado as well as the Harrier, and after the 2010 SDSR when the RAF threw the Harrier force 'under the bus' the tone of those on the light blue side about what they want to use the aircraft for feels distinctly land locked...
...In this context, it is understandable that the Navy would be looking elsewhere for a partner to help fill the decks of the QECs.