I think it's the /key/ to how the Rebellion started. I don't think Rhaegar randomly thought to run away with Lynna because of her courageous display, nor do I think he was fulfilling prophecy. I think Areys wanted Lyanna captured after figuring out who she was the mystery knight.

There's a massive political sub plot beneath all this. Areys was paranoid about others making alliances. The Stark-Baratheon-Arryn-Tully alliance was a huge threat. Areys' appearance at the tourney changed everything. He stopped his son possibly conspiring against him and hesingle handedly forced Tywin on his side at the via Jaime. He found a reason to capture Lyanna and subsequently stop the Baratheon alliance and submit the Starks. This caused Rhaegar to intervene and take Lyanna. Areys most likely blamed everything on his son, whilst serving his own purpose.

I think a war was coming and everyone could see it. Rhaegar was wary of his father's growing madness while Areys was paranoid about everyone and everything. Of course we're missing details here, but there had to be a reason for all the alliances going on. Rhaegar tried to prevent a war by overthrowing his father and aligning with the other houses but his father out-strategised him.