GarenxKatarina is canon and it's a pretty big problem in a serious setting

Garen is a paragon of the Demacian values of Honor and Justice who's cause is so noble that even Kayle makes complimentary remarks towards him. His morality is inherent, it is clear he believes violence is only necessary to do what is right and protect the weak and innocent. Motivations are, for all intents and purposes, the entirety of a character. Garen is all heart and integrity, it's _very _ hard to argue that he has any trace of malignancy.

Sooo let's delve into the glorified Serial Killer, Katarina AKA the problem with this little union.

Katarina's purpose is quite concisely stated to "become a sinister weapon". She takes pride in her abilities to kill people and is even overzealous in this, to her own detriment. She often slaughters Demacian soldiers (Who again fight with morality, and she is also on the engaging/offensive side) and it is clear that she's sickeningly sadistic based off of her short story and the Legends of Runeterra interactions. She is obviously extremely evil and it's never suggested she is anything but evil, barring a very flimsy "duty" to Noxus, which seemed more like self-justification than anything.

Katarina is the epitome of a Sociopath and obviously a horrible partner for literally anyone. Their relationship makes absolutely no sense, Garen should have nothing but fervent contempt for her and no amount of development between these two will fix that. None. There's no point in writing seriously-toned lore if your characters don't make sense, and this is a particularly egregious inconsistency.