The crux of this situation is naturally money. The Heat offered Wade a contract worth $10 million annually, half of what he made this previous season and that steep of a drop offended and angered Wade (even as the franchise was planning to counter-offer a higher number). Considering that Wade has chosen to take less than the maximum in order to allow the team to bring in two over his past three contracts, forcing him to take such a steep decline in his contract doesn't seem right.
Now I understand that the Heat don't want to have to go through what happened with Kobe Bryant and his final contract negotiations with the Lakers. In the end, the Lakers way overpaid their star and ended up with a contract albatross as the quality of the team sharply declined. Considering that Wade is 34, has had a number of injuries and has a lot of miles on his body.
But while Wade is not the star he once was, he still is very good. His numbers have stayed pretty consistent despite moving further into his 30's and last season saw him play the most game he has played in five years. Meanwhile, the Heat came pretty close to getting back to the Eastern Conference Finals by falling to the Toronto Raptors in seven games in the Conference Semifinals so it's not as if the team was a disappointment (like they were the season before).
Not to mention that money is not exactly in short-supply this summer. As the salary cap has sharply increased, teams are spending money like drunken sailors. Granted with the higher salary cap, these contracts (mostly) aren't as bad as they seem but still, should Wade really be making much less money than say Aaron Afflalo, Evan Fournier, Kent Bazemore and the same amount a year as Jared Dudley?
The Heat have professed that it is their intention to bring Wade back in what could be his final contract for his tremendous career but I think their actions thus far raise the question in how truly serious are they?