Ok.... what the heck it is a holiday in USA...
The "story of Yag vs. Plush" started decades ago, when they both were A. Mishin's students. Yag was born in St. Peterburg and was with Mishin and his #1 student, and then Plush came, as an 10-11 (?) year old boy from a remote small town, and had to live alone without family in order to train at that rink. Plush was 2-3 (?) years younger than Yag. Mishin found Plush to be very talented and started spending lots of time on him. Yag hated it, and started to OPENLY bully and hurt Plushenko. He was hitting him when no-one was watching and then telling people "he just fell on his own".
Plush's interview from the 2000's...
https://www.kp.ru/daily/23963.3/72675/
Also as a proud locally born St. Petersburg-boy, Yag resented that a small town outsider is "crowding his city and the rink". He, and other boys at the rink, used to corner Plushenko and say "go back where you came from, out-of-towner".
http://www.spletnik.ru/buzz/8166-kto-kogo-aleksey-yagudin-protiv-evgeniya-plyushcenko.html
Mishin would not give up on Plushenko, and Yagudin got pissed off and went to Tarasova. Then skipping to Olys 2002, the men's event was "Plus vs. Yag" and the whole media hoopla bating two men against each, plus RABID FANS of both engaged in a war.
When Yag stopped skating competitively and started to commentate on TV while Plush was still skating, Yag was full of negativity against Plush at every chance he had. Also, Yag was skating in and working for Averbuch's shows. Averbuch is tightly connected to Russian Channel 1. Russian Channel 1 would hire Yag to commentate. So there was a 3-prone block against Plushenko: Yag putting him down, Averbuch not inviting him to skate in his shows. Channel 1, who had Averbuch and Yag under contract for "Ice Age" also leaned against Plushenko in their decisions and commentary.
During the Olympics where Plushenko's rival was Ivan, Yagudin took a stand against Plush, belittling his quad, etc..
The fight in the media continued "he-P said vs. he-Y said"..
Then Plushenko met and married Yana, they organized their own shows, started to plan the development of a skating school. Plushenko's shows became more and more successful, and a competition to Averbuch (thus Yag)... Plushenko's finances improved, he had investors interested, his wife is a society person with media work and connections, etc..
In the mean time, Plushenko continued to receive surgeries and medical treatments for his injuries, and then announced he will be skating in 2014 Olympics. Many doubted he could given he had metal screws and roads in his spine... But he was sure he can do quite well at least in Team Event, and possible in Singles event. There was only 1 spot for Men, and Kovtun also was a contender. But if Plush skated Team Event, there was no spot for Kovtun.
Yag naturally took Kovtun's side, and stated his position (aka greedy selfish Plushenko, poor Kovtun) on every channel he could.
The war continued after 2014... He-P said, He-Y said... on and off, at every opportunity, and interview, but in their defense, the Media was baiting them both to get a "juicy story", and asked directly about "the conflicts between them".
When Plushenko's Academy developed and became even more successful, Yag continued to make fun of it, saying things like "it's a kinder-garten on ice for rich people's children", "it's just a play ground, no serious training takes place", "how can Plush call himself a coach, when he is constantly doing shows", etc...
(and the above is a short version... if i do a long version, it will be at least 10 pages, with many articles and interviews and videos attached....

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So, what happened now: The Academy Ice rink, during late evening hours, was rented out for a commercial venue. A private company hired it for a Corporate Celebration, and hired Yagudin to perform on the ice.
Plushenko saw that Yagudin just showed up at his Academy, and (summary of tweets, in my own words) said: "you have no shame to show up here at my place, after all the things you said and did against this Academy and me". And then his wife Yana got involved, and she is not shy....