As a diehard Packers fan here is my take. This is based on all of the actual reports of what happened, by trustworthy, reliable sources. Most of what has been out there this offseason is not based on any facts or information, as is usually the case with offseason, "clickbaity drama" stories.
Brian Gutekunst (the GM) drafted Jordan Love after trying to trade up for a WR multiple times, to no success. They could not find a trade back that was going to be worth the value, and the only player left on their board with a high enough grad was Jordan Love. They traded up to take him. Brian confirmed the attempts to trade right after the draft. The pick made sense at the time, as Rodgers had not been playing at his MVP level for a few seasons prior. He was not playing within the rhythm of the offense, and too often he was trying to make off-script plays. It lead to him playing below his standard, which, to his credit, is still better than most QBs in the league.
Fast forward to the 2020 season, Rodgers played to Matt LaFleur's script. He played within the structure of the offense. He played lights out by doing so and won MVP, putting up arguably the best season of his career. There is no doubt in my mind that this change of play style was at least partially to do with his potential successor being in the building. It motivated him to play with timing and rhythm in mind. Towards the end of the season, he wanted a guarantee that he would be in Green Bay long term, as his contract runs out of guaranteed money after this season. That means GB could do whatever they want with him past 2021. Green Bay initially denied him that request and wanted to keep all options open, and they just wanted to restructure his deal. Later on they offered him an actual contract extension that he rejected.
That is all stuff that has been pretty much confirmed. What HASN'T been confirmed is that he asked for a trade. According to reliable sources, he never did. I have also never heard from a reliable source that he's told teammates that he doesn't plan to be back in Green Bay. For those thinking Adam Shefter is a reliable source, a while after "breaking" the story on draft day, he told Dan Patrick that this didn't come from Rodgers, and it didn't come from the Packers. He even said, "Dan, there was no source!" Shefter admitted that this was all based on what he'd been hearing and it was based on observations. So his "breaking news" was actually just his observations and what he'd been hearing.
Another lie that was reported was that Rodgers wanted Brian Gutekunst fired. This was confirmed to be made up.
Here is where my personal thoughts come in. Rodgers is not thrilled with the higher-ups in Green Bay (probably Gutekunst and Mark Murphy, the team president). They haven't communicated with him as they should with a superstar, face of the franchise athlete. But could Rodgers have come out and cleared the air? Absolutely. The blame is on both sides, but I don't believe things are as desperate as some guys like Mike Florio think they are. It's the NFL offseason, and what gets clicks? Overblown stories about Aaron Rodgers wanting out. A lot of the stories and reports are the exact same things we knew a long time ago. Stories from national NFL media have been totally different from local reporters who know more of what's going on. And they've been different from his teammates who have actually spent time with him this offseason, such as John Kuhn, James Jones, and AJ Hawk. All three of them have spent time with him and have said they think he will be back and the situation is fixable.
Now, after having watched Aaron Rodgers in press conferences and media events for years, I know that Aaron Rodgers likes to have fun with things like this. He like to troll. The "I'm Offended" shirt is totally a troll move on his part. He knows that it will blow up into something it's not, and he loves that. The media played it up as a response to Mark Murphy calling him a "complicated fella", but the interview he wore the shirt in was actually taped before Murphy made the comments.
I believe Rodgers will be back with the Packers for training camp. He may sit out a little bit, but I believe skipping minicamp and OTAs earlier this offseason was more about having the time off and spending it with his fiancee. I think he will play for the Packers for another season, and he will be traded next offseason.
So my summary: Both sides are at fault. However, the story has been blown up to much more than it actually is.