Why the Trailblazers do this:
Dame wants out, but Scoot Henderson, Anfernee Simons, and Shaedon Sharpe will still make up a small backcourt. The Trailblazers cannot take a gaggle of talent in exchange for Damian Lillard. The Heat have assets that match Dame's contract, but not the Blazers' lineup. Additionally, the Trailblazers can no longer assume that Jerami Grant will want to stick around too. Our team's timeline does not match Grant's trajectory. This trade allows the Trailblazers to acquire talent, while sending Grant to a contender, and Damian to Miami hopefully to compete in the NBA Finals.
Why the Heat do this:
Damian is the best clutch shooter in Trailblazers history. If Miami finds themselves down two points before the end of regulation, give Dame the ball. He can hit from 50' without flinching. By sending their tradable assets to other teams, which gets the Trailblazers the talent and size they need, Miami creates a win-win solution for both franchises.
Why the Nets do this:
Grant is a beast! I really wish the Trailblazers could have acquired enough talent to keep Dame in Portland because the Dame-Grant show was fun to watch. Alas, Grant is 29 y/o, and his timeline, despite the great contract, does not fit the Trailblazers' roster. Grant, however, would support a strong frontcourt in Brooklyn that already features Nic Claxton and Dorian Finely. Additionally, the Trailblazers would take on Spencer Dinwiddle's expiring contact, which I doubt would get renewed in Portland. Better still, the trade helps Brooklyn improve at point guard with the addition of Kyle Lowry.
Also, Jamie Jáquez and Amen Thompson make this trade fail because they're recently signed rookies. The @Fanspo trade machine will not allow transactions involving rookies for another 30 days.