Yuuri And Viktor Never Were A Coach And A Student Who Happened To Fall In Love With Each Other, They

Yuuri and Viktor never were a coach and a student who happened to fall in love with each other, they became coach and student because they were in love, and this was the best thing that could have happened to them.

Yuuri has been infatuated with Viktor since he was 12. (I'm using 'infatuation' because he didn't know Viktor on a personal level so his feelings for him could only be superficial/parasocial). At the banquet, he first hit on Viktor, then asked him to be his coach. That night, Viktor fell in love with him (on a superficial level, too, of course, because he didn't know Yuuri, either). Hence, when he came to Japan, he was very explicit about wanting to coach Yuuri and getting together.

He says "Before we start practising, let's build a relationship of trust first" while actively flirting with Yuuri. So yeah, he definitely wants both.

Of course, Yuuri forgot the banquet and needs to figure out his feelings for Viktor before he can act upon them, but this doesn't erase these feelings, and like Viktor's feelings they develop over time from infatuation into true love.

Yuuri and Viktor benefit from both aspects of their relationship, which isn't a given when a couple works together. Without Yuuri, Viktor would have never considered coaching, and he enjoys coaching Yuuri tremendously. With Yuuri, Viktor finally can be himself.

Yuuri, on the other hand, becomes more confident, explores the different kinds of love he feels, and even breaks Viktor's world record. Especially that last thing wouldn't have happened if being lovers AND coach&student hadn't worked out. Plus, both learn to open up and grow as persons through each other, which contributes to the success of their relationship and makes their love even more beautiful.

One side note on the meaning of 'idol' in this context:

The Japanese word used in the anime is 憧れの人 which implies more than admiration. It implies that Viktor is someone Yuuri admires, but with an underlying not-further specified yearning (check also this post for reference, from my own studies of Japanese I can say they did a great job).

As episode 1 progresses, we see the layers of this yearning. Yuuri skates Viktor's routines to become more like him, but then we see him skate THE VERY ROUTINE THROUGH WHICH VIKTOR EXPRESSES HIS YEARNING FOR A LOVER AS IF ANSWERING HIM. You can't make it more obvious.

Plus, this scene *coughs*

While I believe there are people who would hit like that on an athlete they idolise, I doubt someone with Yuuri's personality would. Call it infatuation, call it star-crush, but the not-even-subtle subtext is very explicit about how Yuuri feels about Viktor. Viktor isn't simply an idol to him but a human being he shows an interest in.

'Idol' is an okayish translation, but it takes away nuance and downplays the intensity of Yuuri's feelings. So please be careful with this one.