Fans like it because it shows strong bonds. Harry has been through so much, and having overprotective mates gives him a support system he really needs. It's a way of seeing him cared for deeply.
There's a fanfic titled 'Overprotective Bonds'. It delves deep into the relationships Harry has with his mates. His mates' overprotectiveness stems from their deep love and loyalty towards him. They go to great lengths to keep Harry out of harm's way, like accompanying him on dangerous quests and fending off dark wizards.
In some versions, Neville could also be one of Harry's protective mates. Neville, who grows in courage throughout the series, would be willing to stand up against any threat to Harry. And Luna, with her unique perspective and magical abilities, might also be part of Harry's protective group.
In some fanfictions, Harry might be overprotective of Hermione because of their strong friendship. They've been through so many dangerous situations together in the original story. Harry values Hermione deeply and has seen how vulnerable she can be at times, so he feels the need to protect her.
He might be shocked at first. It's not every day you find out you have mates. He could be a bit clumsy around them, not knowing how to act. Maybe he stutters when he tries to talk to them or gets all flustered.
One common theme is loyalty. The three mates are often extremely loyal to Harry and vice versa. They stand by each other through thick and thin, whether it's against dark wizards or school bullies.
Friendship is a very common theme. These fanfictions often show how Harry's mates are there for him in times of trouble, like when he's facing a difficult task set by a teacher or when he's in danger from dark forces.
One great 'harry has mates fanfiction' is 'The Bond of Brothers'. It shows how Harry forms deep and unique friendships with his mates at Hogwarts. They go through various challenges together, like facing a new dark wizard threat in the Forbidden Forest.
Since I don't have the details of this fanfiction, it's hard to summarize. However, if it follows the common tropes in fanfiction, it could be about how Harry meets these three females, how they form a bond, and what challenges they face as a group. It might also explore their individual personalities and how they complement or clash with Harry's.