Arnold's sentiments echoed those of Tony Gustavsson, whose contract as head coach of the Matildas expired following their group-stage exit from the Paris Olympics.

In a round-table discussion with media before the Games began, Gustavsson was asked about his future with the team, and whether a contract extension hinged on the results of the tournament.

Instead of answering definitively, the Swede responded with the questions he'd been asking himself in the months leading up to the tournament: regardless of their final standing, was he the best person to take them forward? Was he the best motivator, the best innovator, the best opportunity for progress? Or was he standing in the way of the person who is?

"It's not about what I want," he said, "it's about what's best for the team."

For all their differences, the tenures of Arnold and Gustavsson in charge of Australia's national teams have, in hindsight, mirrored each other's in multiple ways.

Both were hired at a time where the sides were struggling for mainstream recognition and popularity; their results were flat-lining as they navigated a bumpy transition from one generation to the next; they had multiple World and Asian Cups on the near horizon; and their youth sides were either stumbling at major tournaments or not qualifying for them at all.

Over the course of their stints (Arnold for six years, Gustavsson for four), each tried to evolve their teams tactically and stylistically, knowing they needed to break the national habits of directness and athleticism that were always exposed on the international stage.

And yet, despite good intentions, their greatest moments in charge — the Socceroos at the 2022 World Cup and the Matildas at the 2023 Women's World Cup — emerged not through footballing ingenuity, but rather through embracing the emotions of their sides: their passion and character, their grit and their drive, their bonds to one another and to the nation they represented.

But once they had exhausted the emotional energy of their teams, both coaches were subsequently found tactically lacking, watching as their teams stuttered through an Olympic group stage and World Cup qualifying, and realising, at one point or another, that there was nothing more they could do, no matter how much more time was given to them.

Their legacies, as perhaps all coaching legacies are, will change depending on how you look at them.

A graph of the results of both teams would appear similar to each other, dipping in some places and soaring in others. Each had a major tournament peak, but also major tournament troughs. Their results in friendlies were hot-and-cold, too, but there was a sprinkle of performances against highly-ranked nations that gave us a glimpse into a possible future where Australia are no longer minnows on the world stage. 

Both coaches oversaw history-making win streaks, tournament milestones, and the introduction of a new crop of young players who will be the custodians of these teams long into the future.

Statistically, Arnold and Gustavsson were two of the most successful coaches in their respective programs in terms of their win-loss ratios. 

They both took their teams to their best ever finishes at a World Cup and, in the case of the Matildas, the Olympics, too. Arnold steered the Socceroos through a world record win streak during World Cup qualifying, while Gustavsson oversaw a run of results against the hardest string of opponents in their history, before their transformative home tournament.

And yet, despite all this progress, all these numbers, neither have any silverware to show for it. And if that is the way in which you measure success, then perhaps both of them will always fall short.

But there are other ways in which Arnold and Gustavsson will be remembered, ways to appreciate their legacies and remember them with fondness.

At a time when the Australian game was fading in national relevance and cut-through, both coaches were able to reconnect the Socceroos and the Matildas to the national psyche again.

Their players went from largely unknown figures to household names and personal heroes. Their games at the most recent World Cups saw tens of thousands of people flood city streets and squares to watch on giant screens in the middle of the night. Their jerseys sold out, their faces were splashed across magazines and television, and their social media followings skyrocketed. 

Arnold and Gustavsson were not responsible for that rejuvenation, but they were part of it, lending their own personalities and emotions to the bigger cause of making Australia care about its national soccer teams again. 

Tunisia, Denmark, Argentina; Canada, France, England: these tournaments, games, and moments will live long in the memories of the Australians who watched them, as will the two men who made us believe, even just for a little while, that we could be giants.

For many rusted-on fans, who have followed the desperate ebbs and flows of the domestic game, those who can break through the "grass" ceiling and connect the country to its most-played grassroots sport hold a special place in our hearts.

On multiple occasions, they also advocated for more investment from governments and businesses and brands into football. Whether it was the national teams, the A-Leagues, youth pathways, or community football, from facilities and infrastructure to full-time contracts and more opportunities to play, both Arnold and Gustavsson used their voices on behalf of the game that so often struggles to be heard.

But they are not the ones to get us there. We are. 

While their position at the top of the pyramid may have separated them somewhat from the tangle of issues domestically, it did give them both an eagle-eye view of the state of the game down below, and the things that must change in order for Australian football to grow.

They see the urgent need to develop our youth pathways, to accelerate and expand the A-Leagues, to professionalise more coaching opportunities, to remove barriers to entry at grassroots level, to build more fields and more change-rooms, to tear down the walls of Australian soccer's various kingdoms so that the game can move forward together.

Will we listen? Will we act? Will we learn from these past few years and set the game on course towards a bigger, brighter future?

How will FA appoint their replacements? Who do they aim for? Do they just want coaches? Or do they want national leaders, emotional motivators, cultural storytellers, and political agitators? 

Do they want people who can not only coach the game, but change it, too?

Because Arnold and Gustavsson do not want their legacies to only be emotional. They want to see it manifest in front of them: the fields, the players, the competitions, the trophies. The things that the rest of us are now responsible for building upon in the wake of their leave.

They took these jobs because they believed, and still believe, in the potential of Australian football, and the idea that our teams can be truly great. That the sport can be the biggest in the country. That we are not just a nation that plays football, but a true football nation.

And while their tenures may have come to an end, the ambition and belief that they inspired in ourselves will survive long after they have gone.

Their legacies will be defined by what the rest of us do with that belief next.