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 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.
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.
'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.
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.
Voldemort's remaining Death Eaters could be the ones. Even after Voldemort's defeat, some of them might still be lurking in the shadows. They could force Harry into marriage as a form of revenge or to try and corrupt his good nature. They might think that by making him marry someone of their choosing, they can turn him to the dark side. Also, a group of radical pure - blood supremacists who see Harry as a threat to their traditional values might force him into marriage to try and subdue him and make him conform to their ideas.
In some fanfiction, this could happen due to a power play. Maybe Draco's family still has some influence and he uses it to force Harry. It could also be a result of a misunderstanding or a dark plot twist where Draco believes he has no other choice to get what he wants.
In some fanfictions, it could be a plot device used in a time - travel scenario. Harry is sent back in time and for some reason, he is forced to touch a younger version of a character. This could be Dumbledore as a young wizard. The touch might be forced by a temporal anomaly or a spell set by a time - traveling antagonist. This forced touch could then have a profound impact on the timeline, causing changes in the future that Harry has to deal with. It could also lead to a deeper understanding of the character's past and how it shapes their future actions.
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.
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.