'Him' could be a centaur. In the Harry Potter universe, centaurs are intelligent and powerful beings. Harry might ride a centaur in a situation where he needs to quickly cross the forest and the centaur's speed and knowledge of the terrain would be very useful.
It could be a house - elf. Maybe in a unique fanfiction idea, a house - elf has some special ability that allows Harry to ride it, like it can transform into a flying creature for a short time. This would be a very different and unexpected take on the concept.
The 'him' could be Draco Malfoy. It would create an interesting dynamic as they are usually rivals. Maybe in a situation where they are forced to work together on a secret mission for the wizarding world, and they end up in close quarters, rubbing against each other accidentally. This could lead to a change in their relationship, from enmity to a more complex understanding.
The 'him' could also be Snape. In a fanfiction, a spell or a magical experiment could go awry and force Harry to touch Snape. Given their complex relationship in the original series, this forced touch could be a catalyst for a lot of emotions. Harry might finally understand some of Snape's motives or Snape might have a moment of vulnerability that changes how he views Harry.
It could be Voldemort in a really strange and dark fanfiction concept. Maybe Voldemort has found a way to magically force Harry to perform this action as a form of humiliation and domination. This would be a very different take on their relationship compared to the original series.
One interesting scenario could be that Harry Potter rides a magical creature in a race against time to save Hogwarts. Maybe he rides a Hippogriff and they soar over the Forbidden Forest, facing various obstacles along the way.
The man could be an Animagus who has the form of a large, rideable creature. Harry might not know at first and then discovers the truth during the ride.
He could use his wandless magic. Harry has shown some ability for wandless magic before. He might use it to unlock the doors or create distractions to escape. For instance, he could make a loud noise to draw the Muggles away from the exit and then make a run for it.
One possible plot could be that in a magical accident, Harry Potter finds himself in a situation where he has to constantly be in close physical proximity to another character, like Ron. Maybe they are stuck in a shrinking charm situation and have to rub against each other to stay warm in a cold, magical environment. This could lead to some humorous and heart - warming conversations as they deal with this strange situation together.
One possible plot could be that a dark wizard has somehow magically compelled Harry Potter to perform this action against his will. However, this goes against the core values of the original series, so it would be a very dark and twisted fanfiction. It might involve Harry having to fight against the magical compulsion through his own inner strength and the help of his friends.
Maybe it's a magical portrait in Hogwarts. Some portraits in Hogwarts have a lot of knowledge and wisdom. One particular portrait of a former great wizard could notice Harry's need to fly without a broom. This portrait could then guide Harry through a series of magical trials and lessons, teaching him how to tap into his inner magic and fly without the aid of a broom. It would be a long and difficult process, but Harry, being determined, would eventually master it.
Luna Lovegood might also be a likely candidate. She has a unique perspective on the wizarding world and is not bound by the traditional views. Luna could offer her creativity and her ability to see things that others overlook. Her friendship with Harry could easily lead her to support his new grey faction and contribute in her own strange but wonderful way.