Well due to the fact of another lockout Kovy got to play in the KHL for the first time so he didn't sign in the first place because he played in the NHL his whole life. It's also considering the fact that NJ did give him the contract that was most financially secure for his future.
After the lockout he was offered a lot more by the KHL because he was really popular in the country and it was noticed by the team. He felt comfortable playing there and it all contributed to his departure. Yes, if you were in Kovy's shoes you would do the same exact thing. It's funny how owners have the right to break up contracts by buying players out but if a player goes ahead and gets MUTUAL AGREEMENT with the ownership to leave the league he somehow is violating something. He didn't violate anything, the owners let him go and he had very good reason to good. You can only go against that because you have the bias of being a fan on a team and not being the individual involved. Family vs. a contract that was already tampered with by the owners after the lockout? I'll go with family like most loving people would.
And come on, I will give you an Elias season being better (although he did get to play with 2 top players that had great chemistry with him) but an no point did Parise even come close to Kovy's play. It's like the Patrick Kane vs. Johnathan Toews debate (however their levels of play are a lot more closer in terms of skill) wherein Kane is just more dominant on the ice than Toews. Yet, Toews is overrated and more people consider him better. Parise never came close to what Kovy did, there is a reason this team went first to second round exists constantly in the playoffs where Parise never elevated his game in the playoffs while Kovalchuk elevated himself to another level without a back.