I think the story here is great. Inori wanting to skate but feeling a bit too old now really gets you to root for her. Then Coach Tsukasa comes in who has a similar story but in his point of view she has enough time since she was younger than him when he started skating. With Coach now taking Inori seeing her put all her effort into improving is so motivating and really locks you in. Inori and Tsukasa's dynamic is very great across the anime so far and very endearing.
The conflict developing with Inori finding a rivarly with Hikaru who is best upcoming skater coached by a gold medalist Tsukasa knew during his career is amazing. Having Tsukasa and Hikaru's coach, Jun, have different ideas on coaching where Jun believes that Hikaru can't possibly catch up to Hikaru since she has already talent and is coached by him. All that being said the beef isn't like too intense, like they don't hate each other, but it raising the stakes enough for it to be exciting. On Inori and Hikaru's side they are more friendly rivals with Hikaru interested to see Inori improve and Inori amazed by Hikaru skill wanting to be able to do a performance as amazing as her. It's a heartfelt but intense rivalry that I love.
I discussed the main characters a bit in the story section but I could talk more about them. You might coach Tsukasa's rivalry with Jun could possibly lead to his emotions bleeding into how she coaches Inori but it doesn't. He is soley determined to get Inori to acomplish her goals. Inori's drive is also amazing. Seeing her put in all the effort she can while being amazed by everyone she is able to witness in competitions and at practice. You can feel the emotions she feels when she messes during a performance or is struggling to perform a new move. The side characters also a brimmed with personality and although we can't focus on them too long we see their struggle as well and feel the effort they put in their performances. Really gives all the characters great traits you can root for.
The world is growing at a rate I can appreciate. As someone who doesn't know much about ice skating it is explained well so I can understand the point system and when to get nervous and when to get excited. On top of that the world is gradually expanding as Inori is able to place well at higher level tournaments. We see she heading down a path where as of now she going to go head to head with Hikaru. The expanding cast also doesn't feel like too much. It's done at a pace that gives characters enough time for you get familar with. The world has been established well.
The music I remember being good but of course the most memorable pieces of music are the ones that play during the skaters performance. They very awsome and add the performances in a way that makes even cooler. Very nice ost that keeps even more locked into the anime.
Animation is great throughout the show. The animation during regular dialouge and walking scenes are good. The best of the animation is during the performances. The use of CGI is amazing showing off the moves done by the skaters. Brilliantly done showing off the effort in the movements while showing the mistakes impact very effectively. Great animation.