The reason the Thrashers were able to relocate after selling was because of poor fan support.
Absolutely not.
The reason the Thrashers were able to relocate was because of massive in-fighting among ownership within Atlanta Spirit, who also owned the Atlanta Hawks NBA franchise, as well as the arena (the infighting started on the NBA side of the business, and featured partner Steve Belkin on one side, and the rest of "Atlanta Spirit" on the other). They were in court for years trying to force a buyout of Belkin's 30% stake in Atlanta Spirit, and caused massive brand damage in the process as Atlanta Spirit, the team's owner, publicly claimed that "hockey would not work in Atlanta" in order to reduce the value of the investment so that when they bought Belkin out, it would cost less since the asset would be publicly devalued.
This went on for HALF A DECADE. Finally, when Atlanta Spirit bought out Belkin, fans had been told for half a decade BY THE OWNERS that the Thrashers would never succeed, so they stopped going. It didn't help that Atlanta Spirit had never wanted the Thrashers, they had bought Phillips Arena and the Hawks from Time Warner (after the massive AOL flop) for the NBA team, and were forced to take the Thrashers as well because they were the other tenant at Phillips Arena. The only people in the Atlanta Spirit group who even had the faintest interest in hockey were Bud Seretean (who died before the Thrashers were sold) and Belkin (a Boston native), who was forced out.
After the Belkin buyout, Atlanta Spirit wanted to rid themselves of an asset they never wanted in the first place, and put the Thrashers up for sale... but also refused to let the new owners use Phillips Arena as a home for the team. Basically, that left Atlanta with a hockey team but no hockey arena to play in. Since arena ownership exists outside of the terms of ownership in the league, the NHL could not force them to allow the Thrashers to play in the building.
The NHL had an NHL team in a city with no arena to play in for the immediate future, and no support to build a new arena for the long-term future. So they moved the team.
And even as I post this, my description of the Atlanta relocation is the short, ultra-concise version of the story. You could write a book about everything that led to the Thrashers move to Winnipeg. Heck, just the part of the story where Atlanta Spirit buys the Hawks/Thrashers/Phillips Arena package would be it's own novel.
Saying "Atlanta lost the team because bad fan support" is such a cop-out answer to a much more detailed, nuanced, and ultimately disastrous story that features toxic ownership, debilitating in-fighting, and overt, purposeful brand destruction.
TL,DR: The Thrashers left because, due to terrible ownership, the team no longer had an arena to play in, and the league couldn't force the arena owners to let them use their arena.