About

The rivalry was basically started by Shinn Asuka. He was angry with the Freedom (and Kira who he didn't really know O_o) since he killed Stellar, who was the pilot of the first Destroy Gundam. The Minerva crew also thought that the Archangel and the Freedom's actions are bringing more chaos into the battlefield.

Second, Shinn wanted to defeat him since he was the toughest opponent out there. From my point of view, the rivalry seems more of who's the best xP.

Be the way, I named it 'Grudge Match' since it seems those two will have some grudges in their rivalry >_<