Game Of Thrones: 10 Most Believable Fan Theories
2. Southron Ambitions
The accepted reasoning behind Robert's Rebellion is that Rhaegar Targaryen kidnapped his betrothed, Lyanna Stark. This caused her brother Brandon to march on King's Landing and demand to face Rhaegar, for which the Mad King Aerys II Targaryen had both him and his father Rickard executed, kicking off the war led by Robert, Ned Stark, and Jon Arryn. Before that, though, there may well have already been a plot to remove Aerys from power. This is what Lady Dustin refers to as Rickard's 'southron ambitions."
Although it's never questioned by the characters we meet in the series, it is actually quite uncommon for great houses to marry outside of their kingdom, with them usually being betrothed to bannermen. So for example, a Stark would typically marry another Northern family; Hoster Tully married a Whent; Steffon Baratheon married an Esterman; and Tywin Lannister went so far as to marry another Lannister.
It seems unusual that this would suddenly change for no reason, yet Robert Baratheon is betrothed to Lyanna Stark, and Brandon Stark to Catelyn Tully. Even before this, Robert and Ned were sent to the Vale to be fostered by Jon Arryn, strengthening links between the three houses.
The heads of these houses - Rickard, Steffon, Jon, and Hoster - all fought together in the War of the Ninepenny King, and it seems that they colluded with their plans to overthrow the rule of Aerys, and have Rhaegar (a far more sane, liked, and noble person) rule instead, with greater freedom and power for their individual kingdoms. Obviously that plan went out the window when Rhaegar 'kidnapped' Lyanna, Aerys chose fire as his champion in a trial by combat, and Robert's Rebellion began.