Because she had a Lucario, and they wanted to write an arc of some sort around a character struggling with Mega Evolution, and I guess just saw it fit to be the character who's most tied to it in the games. It's not that they just picked a random side character and were like ay let's give this one an arc for no reason.
Now, you can say that it would've been better if they did the whole Mega Evolution struggle story with Ash, but they probably wanted to do it early while Megas were still being established, which would result in Ash having a Mega tier Pokemon on his team for most of the region, which would be even harder to balance than Pikachu (or they'd have to release it, like Goodra). It is much more interesting to have Ash DEFEAT a Mega without one of his own at that stage, and the Korrina arc also served to set her up as a more personal obstacle for Ash to overcome (kinda like a rival, no one complains when those get focus). We've seen him lose to her, we've seen her struggle afterwards and become even STRONGER, can Ash defeat her? At that point we didn't know, could've very well been a tie badge like VS Maylene, or even a pity one for good effort, for putting up a good fight against a Mega and for helping Korrina achieve that power in her arc. It was exciting.
I won't make excuses for things people wanna criticize (Clemont and Serena lacking focus at that point was true, but they did get better so in hindsight I don't think Korrina ruined them or anything), I'm not saying the arc is some master piece that you have to like, but there're more thoughts put into building these shows than you think and more limitations to consider, I see people completely brush the Korrina arc off simply due to it not being about main character way too often, it doesn't even make sense considering the show mainly revolves around meeting new people weekly, if we didn't focus on Korrina for multiple weeks we would've just gotten that many more COTD's.
sorry for an off topic wall of text, if anyone feels particularly strongly about this feel free to pm lol