Why?

[Romeiro Celtic]

Why did the Nuggets started rebuilding after the 2012-2013 season?? That was a great season, winning 57 games, COY award, great core, but the only bad thing was that first round upset against the Warriors. What actually happenend??

[NuggetsWY]

Why did the Celtics begin to rebuild in 1970?
Why did the Celtics begin to rebuild in 1977?
Why did the Celtics begin to rebuild in 1993?
Why did the Celtics begin to rebuild under Doc RIvers?

Probably the same answer the Nuggets would give; the team was not doing well enough.
Would the Celtics fans be satisfied with perpetual 1st round exits?

The Nuggets began a rebuild in an attempt to build a better team.
It seems like an obvious answer. If you are looking for a different answer, please make your question more specific.

[The Rebel]

they didn't start rebuilding on purpose.

Basically the story is that Ujiri got a big offer from Toronto and despite already having a verbal agreement to extend with the Nuggets, so the Nuggets let him out of his agreement and he left.

Karl got into Josh Kroenke's face and aggressively demanded (Karl has said this himself) raises and extensions for himself and his assistants, which pissed Josh off especially since it was right after another 1st round exit so Karl got fired.

Gallo was out for the year, after he got injured late in the 2012-2013 season (which is a big part of the reason the Warriors won that series) it was known that he would be out for most of the following season.

After Igoudala got caught hanging out with the Warriors, and his own cousin was telling Warriors ownership that he was wanting to go there more than one time throughout that series, he played the Nuggets telling them that he was coming back. By the time it was known that he was leaving it was late enough in free agency that we really only had Foye available which was a huge downgrade.

The Nuggets brought in Shaw thinking he would improve the half court offense and the defense, he was a disaster and lost the team pretty quickly. he had no idea how to fit a system around his players, instead trying to run some weird hybrid offensive system that put guys in their worst positions.

They traded Fournier because Shaw did not know how to use him and they got Afflalo who had a terrible attitude and basically forced his way off the team halfway through the season.

Mozgov, Gallo, and Chandler kept getting hurt.

At least half the team openly quit on Shaw, and even had the chant 1,2,6 weeks left coming out of a huddle just before Shaw was finally fired.

Without Karl and his staff to keep Lawson in check he started drinking and lost control.

Their plan was always to make the playoffs every year, but with everything that happened the 1st couple of years after that team it was 1 thing after another.

Even the last couple of years the front office has had every intention of trying to make the playoffs, and built around Gallo and Chandler, despite their injury issues. Finally in December they realized what they had in Jokic.

[youngthegiant]

Technically they didn't try to rebuild straight after, they tried to put together a playoff team under Shaw for 2 years but failed miserably.