Fanships in anime have recently exploded in terms of popularity among multiple forms of media. No matter how long they've been present, they're an essential part of a wider atmosphere. The reason being is that some fans see chemistry in other non-canon characters.
Perhaps the creator of the series happened to make a platonic scene unintentionally romantic in the story, but in the end it doesn't matter because some fans will run with it.
Some fans simply find the main pairing boring or wish to add some spice by throwing in a controversial ship.
10 anime ships that should be canon, featuring Rin and Archer, and more
1) Digimon - Taichi and Sora
Taichi and Sora is an incredibly popular fandom ship in Digimon anime, so much so that Sora's intended, Yamato, is ignored. Some fans seem to think she reciprocated because Taichi and Sora were childhood friends. Taichi seemed to encourage Sora throughout the series as she reciprocated his actions.
These actions could even be viewed as romantic since Taichi and Sora are the leading characters. Usually, the standard romance would have the male lead ending up with the female lead, no matter the circumstances.
2) Fate/stay Night - Rin and Archer
Even though Rin is a potential love interest to Shirou, the protagonist, some fans seem to love her with Archer and her summons. Their arguments and banter seem to encourage fans to ship the two as 'enemies to lovers' is a very popular trope, especially in anime.
Another trope present in this fanship could be the Master/Servant appeal. Power imbalances in a relationship can be very tempting, as its structure will be a hurdle for the couple to overcome.
3) Food Wars! - Soma and Erina
A semi-canon ship, fans were left disappointed when the manga ended in a cliffhanger for the couple. Reasons being, they never confessed to one another, nor did they have any intimate scenes.
The reason why this ship is popular is because at first, they went through the typical enemies to potential lovers route, so much so that fans considered it a beautiful relationship arc.
4) Fushigi Yuugi - Suboshi and Yui
Suboshi and Yui are a popular ship in the anime fandom as it seems to expand on the trope of extreme or obsessive love. Suboshi is excessively loyal to Yui to the point of madness, but this just fuels the fans love for this ship.
It helps that Suboshi does seem to have romantic feelings for Yui, but she clearly doesn't reciprocate them. However, this doesn't stop people shipping them as there's a good amount of pining in this pair.
5) Genshikin - Madarame and Saki
Some fans seem to find this ship endearing and romantic in the sense that it outwardly resembles the 'Beauty and the Beast' trope. While Madarame is not a good looking guy, Saki appears to be beautiful. Their relationship is seen as incredibly endearing and wholesome, unlike the canon pairing.
Another aspect would be the fact that their teasing seems a little too flirtatious at times. Usually, teasing can be viewed as fuel to the fire of many ships, so it's no wonder why they became somewhat popular.
6) Great Teacher Onizuka - Onizuka and Urumi
Perhaps strangely, several anime fans would wish that Onizuka ended up with Urumi as Asuza is seen as a boring love interest. Urumi, on the other hand, is a chaotic soul determined bring Onizuka down with her.
The reason why the ship is popular is because no matter what Urumi does to him, Onizuka is always willing to help her. This would fit into the trope of a woman fixing a man, but in reverse. Several people love a good story of healing a love interest, so it's no wonder this pairing gained some traction.
7) Guilty Crown - Shu and Hare
Hare and Shu seemed to have a good relationship with one another, though Hare was clearly in love with him. She believes in him and will do almost anything for him, though when the latter tries to kiss her, she recognizes that he's using her as a replacement for Inori.
This scene seemed to show fans that she's a much better love interest than Inori. Typically, characters interested in another would simply accept the kiss rather than ignore it, so it was seen as a sign that Hare was a rational and strong character. Still, when she confessed to him after her death, it fueled the ship even more.
8) High school D x D - Issei and Akeno
Akeno and Issei seem to be a very popular ships among fans as they seem to be quite compatible. What appeals to fans is the fact that Akeno has no ill will towards Rias, which increased her appeal.
Another reason that fans find them appealing is because Issei defended her status as a fallen angel, which is seen as incredibly romantic. High school D x D introduced several ships, yet this one seems to take the cake.
9) Naruto - Naruto and Sakura
The Naruto and Sakura ship is a very popular ship in the anime fandom, so much so that fans were upset when he ended up with Hinata. Some fans enjoy this ship because Naruto has been in love with her for years.
Another reason could be the fact that some fans dislike Sasuke because he tried to murder Sakura in cold blood, which she later disregarded as she went on to marry on him. Several fans would like her to have a healthy relationship with Naruto.
10) Bleach - Ichigo and Rukia
Ichigo and Rukia are a very popular fanship and were expected to become canon until the manga drastically changed things. The anime had several romantic moments between the two, though the manga only displayed friendship.
In some cases, however, their friendly moments can be interpreted as romantic in some cases. This ship is popular because their dynamic involves growth and acceptance, which is a key element to romance.