Ok so I know right from the start that some people will disagree with me on this as I know not everyone likes Amourshipping, but I just want to give my opinion. Feel free to share yours as well. Also, there are some spoilers so precede with caution. Anyways, here are my reasons:
1. Serena is the first character whose love for Ash is cannon: So I thought that I'd start off with what I think may be one of the biggest reasons as to why it may happen. In every other Pokemon series, a PokeGirl's love for Ash has always been an assumption. People see tiny clues as reasons to assume someone like Misty, May, etc liked Ash. In XY and XYZ, Serena's love for Ash is made apparent by the writers. This was announced back in XY26 with the interactions between Serena and Miette. Since then, we've seen loads of other clues to suggest that it is very much a thing, such as Serena blushing whenever either Miette makes a comment about Ash or when Ash compliments her on something. Furthermore, we see that other characters in the anime have pointed out this fact. In XY89, Shauna makes a comment about this to which we see Serena clearly embarrassed about it. We also have seen twice that Bonnie knows about it as well (XY79 and XYZ22).
2. Serena and Ash have a longer relationship than any other character: The whole origin to Serena's character is that she met Ash in a summer camp back in Pallet Town. It was at this camp where Ash helped Serena when she hurt her leg. No character has had that kind of relationship with Ash. Serena is the first character to have a backstory connected to Ash, which would make it ideal for the two of them to stay together.
3. Serena is the first PokeGirl to actually be invited by Ash to travel with him: Every other character (Misty, May, etc.) has forced their way into traveling with Ash. For example, Misty followed Ash because he destroyed her bike. Ash never asked her to travel with him.
4. Serena is the only character to have received a gift from Ash: At the end of XY59, aka the "Date episode" (more on that later), Ash gives Serena the ribbon he received from the monorail company (I'm not sure if its a monorail or a train but whatever). No other character has actually received anything from Ash.
5. Serena and Ash go on a date?: I did say that I would get to this. XY59 drew a lot of attention for people because it seemed as though Ash and Serena were on a date (kinda). While it may not have been much, it is something different as we've never seen Ash and one of his female companions go someplace with no one else (people or pokemon).
6. Serena has a rival based solely on her love for Ash: Ok, I know a lot of you are going to disagree with me here, but I personally think that Miette is only relevant to this series for one thing; her interest in Ash. I mean when it comes to performances, it seems as though Shauna or Jesse would be much more of a rival to Serena than Miette (they both have actually won a performance during one of the episodes -> XY59 and XYZ8). Also, the interactions between Miette and Serena have practically centered around Ash (look at XY26, XY79, and XYZ12). However, they do face off in the master class so there is that.
7. Serena's journey is based on Ash: I know that now she has the goal of being Kalos queen, but Serena originally started her journey because of Ash. She wanted to see him again and travel with him. Even after her new goal of Kalos Queen, that still factors into her choices, as seen when she rejects the famous performer's (who looks like Hillary Clinton; I don't remember her name so she'll go by that) offer to train her in favor of continuing her travels with Ash (she remembers why started her journey).
8. XYZ Episode 22, buff said: So I was going to break this up into multiple points but this one episode just shows off so much for Amourshipping that I decided to include it all in one point. First off, in the beginning of the episode, while Ash is trying in the water, Serena gets really concerned about Ash getting sick (Well she got that right). Later, you have the scene between Serena and Ash where Serena thinks Ash grabs her hand and actually sounds like he's about the say "I love you" (we kinda knew he wasn't). But still, Serena's reaction suggests that she still really likes him. It's also really important that Serena is the one taking care of Ash while Bonnie and Clemont get medicine. It shows how much she cares for him. This is backed up even more when Jimmy arrives and Serena pretends to be Ash so that the real Ash can continue to rest up. No other character has done before. Which also leads me into one of my last points about this episode, Serena almost perfectly copies Ash's battling style. Almost every move replicates that of Ash, which shows how much she's learned from him. None of the other female companions have had a battling style similar to that of Ash. All in all, the episode was great for Amourshippers.
So that's about it for now. Let me just say that Serena is different from the other characters. Pokemon has never written a story like that of her and Ash. It's different and frankly it would almost seem like a backstab if Ash leaves Serena behind. But anyways, there may have been a few things that I missed so feel free to let me know. Also, as more episodes are launched, I can see myself potentially making a follow up to this. Until next time.