Rush's Links
To Rush, Holly was always a tough opponent who gave them a run for their money, but even though they won their battles, Rush was admittedly jealous that Holly always seemed to have a better connection with the other minor league leaders. At least in comparison to Rush's own non-existent social life. Ultimately, they were in their own head too much to really see how much their rival was also being affected by the celebrity culture foisted upon them.
They didn't think any of the other minor leaders would care when they up and left their position.
It wasn't until they saw Holly's breakdown on TV that they realized it. At least their own emotional breakdown happened in a much more private setting, and they felt really bad for Holly suffering one of Rush's worst nightmares.
Then they saw the vultures starting to pick at Rush's mysterious quitting, and the comparisons hit them in the face. They left Galar again. Originally, they had planned on just avoiding Holly for the future since it hit them how horrible Rush must make them feel.
But when Life Had Other Plans, they finally get to spend time around Holly as A Person instead of in their celebrity persona, and even though it's really awkward, they do enjoy spending time around them. They hope that Holly can somehow find the same peace they did, but they're unsure if the help can come from them.
Hollyhock has a tumultuous and confusing relationship with their former rival. Rush is the ultimate symbol of all their failures, after all. The one they could never overcome, the one who they always fell short of, the apprentice of the person who destroyed their fleeting success. Holly doesn't truly hate them, but they associate so many negative feelings and thoughts with the ex-gym leader. Being continuously compared to Rush never helped matters. In the aftermath of their disastrous battle against Miles, Hollyhock is eventually given a chance to finally connect as a person with Rush, and it is as painful as it is cathartic. They are frightfully similar, and maybe that explains so much about their shared history. Holly wants to overcome the past, and find peace with their once-rival, but getting there is a difficult and agonizing journey.