The former Tottenham and Norwich City midfielder spent nearly 20 years inside professional football before moving into psychology, performance coaching and business. He has also spent years working with business leaders, and that experience has changed the way he looks back at the game.
His conclusion is striking: football once taught the business world how to coach people. Now, in some respects, McVeigh believes business does it better.
He told Football Presse, "Back in the 1960s, it was really the Americans that started it whenever they started going, hold on a minute, this whole sports thing where you have a coach and the coach helps the people perform, but they actually get quite understanding of the role and really understand the person and keep that going.
"Maybe in the business world we could replicate that model and we could bring in coaches to help our teams perform better and our individuals perform better."
The idea grew. Coaching became embedded in business, with organisations increasingly using mentors and external coaches as part of individual development.
But while that was happening, McVeigh believes football was moving in the other direction.
"As this is happening every single day in the sports world, coaches are improving, coaches are improving, it keeps going. But it's now got to a point where the business world has incorporated this so well that pretty much across most organisations, across most levels, there's some sort of mentor-mentee relationship or an external coach coming in to help somebody perform and improve as part of their personal development plan.
"And in football and in sport now, it's almost starting to become less and less because the coaches are now doing less of the individual mentoring and more of the, here's your stats, here's the numbers, here's the thing you need to do.
"And it's becoming less people-centric than it was 10 or 20 years ago."
For McVeigh, Sir Alex Ferguson provides a simple illustration of what football coaching could be when the relationship between manager and player comes before the numbers.
"You just have to look at some of the characters around the game. Let's say even a simple one, Sir Alex Ferguson.
"He wasn't worried about the numbers and the stats and the distances and, oh, you're into the red-blue zone, so now you have to take a break. And, you know, are you okay in the running session? Let me pull you out.
"No, he's working them hard, but he knew every single thing about every single player that helped that relationship."
The important part, McVeigh says, was not simply that Ferguson knew his players. It was what that knowledge allowed him to do when the pressure increased.
"Because when it came to the hard moments, and he had to dig them out and he had to give them a hard time, he'd built up enough credit in the bank with them, enough of the relationship with them, that he could say, 'Come on, we need to do better.'
"Which still kept them all on the same side because they knew they were all pulling together."
That idea of having "credit in the bank" is central to McVeigh's view of leadership.
A manager can demand more from a player, challenge them, criticise them or push them beyond what they think they can give. But the ability to do that is built over time. The player has to believe the manager understands them and is ultimately working in the same direction.
It is a very different model from one based purely on performance data.
McVeigh's point is not that data has no value. In other parts of his interview, he describes just how dramatically sports science has transformed football. His concern is what can disappear when measurement becomes a substitute for knowing the individual.
The irony, he says, is that the business world has increasingly recognised the value of that individual relationship.
"I think that's the really interesting thing that now I would say the business world do it way better than what football does in terms of that one-to-one coaching."
It also connects to McVeigh's wider concerns about the psychological side of football.
He has previously questioned whether clubs have invested sufficiently in mental performance, but his experience suggests the problem is not simply whether a psychologist or performance coach exists within a club.
The player has to trust the relationship.
When McVeigh returned to professional football and worked with a Championship club, he found players reluctant to reveal weaknesses because they worried that what they said might eventually reach the manager.
That, in turn, makes meaningful coaching much harder.
The same principle applies to the manager-player relationship. If a manager wants to push somebody through a difficult period, there needs to be enough trust for the player to understand that the criticism is coming from somebody who knows them, rather than somebody simply reacting to a number on a screen.
That is what McVeigh remembers in Ferguson.
It is also why his argument reaches beyond nostalgia for an older generation of managers.
Modern football has acquired enormous amounts of information about players. Clubs can measure distances, workloads, heart rates, recovery and countless other physical variables. They can analyse matches down to the smallest detail.
But knowing more about a player does not necessarily mean knowing the player better.
For McVeigh, that distinction matters.
The coach's job is not simply to identify what a player has done wrong or where their performance has dropped. It is to understand the person well enough to know how to respond.
Sometimes that means encouragement. Sometimes it means protecting them. Sometimes it means listening.
And sometimes, as Ferguson demonstrated, it means telling them they need to do better.
The difference is whether the player knows that the person saying it understands them.
That may be one of the lessons McVeigh has taken from spending almost two decades in football and then looking at the game from outside it.
Football helped give the business world the idea of coaching as a way to improve people. But as the sport has become increasingly sophisticated in its use of data, McVeigh believes it should not forget the original principle that made coaching so powerful in the first place.
Know the person.
Then coach the player.