Jango Fett is Not a Mandalorian
From a certain point of view, this is a mix-up asking to take place, with Mandalorians defined by armor that could practically be worn by anyone, regardless of their heritage of belief system. Obi-Wan Kenobi presumed that Mandalorian armor=Mandalorian in "The Mandalore Plot," season 2, episode 12 of The Clone Wars. When beginning his questions about possible rogue Mandalorian agents, his questions about Jango Fett keeping their 'deadly' reputation alive were immediately dismissed by Prime Minister Almec, clarifying with obvious indignation that "Jango Fett was a common bounty hunter. How he acquired that armor is beyond me."
It's here where the plot hole forms, essentially putting Jango Fett's entire story and role in question. To some, the fact that Prime Minister Almec plays with the truth later in the season means he's lying here, too (even if there's no real reason to). But it's possible to make this scene work with the lore Star Wars fans have surrounding Jango Fett. Especially since his embodiment of the perfect Mandalorian way of combat is exactly why he was chosen as the model for the Grand Army of the Republic.
Was Jango Fett Disowned By Mandalore?
This is speculation on our part, making the assumption that the Clone Wars team was hinting at a much larger story--instead of erasing one for kicks. If Almec is one thing, it is performative-ly outraged if it keeps up appearances. Which means his description of Jango Fett as "a common bounty hunter" may have more to do with how he's seen by Mandalorians, than if he was a citizen of Mandalore before The Clone Wars. Knowing what we know about the Mandalore tradition, Jango definitely did the one thing his warrior nation would look down upon. Even if they wouldn't learn about it until an endless army of clones spread across the galaxy.
The Attack of the Clones movie outlines the plan: Jango is hired to contribute DNA to the Kamino cloners, so they can create an army of Fetts. In the previous Star Wars novels, that story was expanded to include the Cuy'val Dar--"those who no longer exist." These were 100 people (mostly fellow Mandalorians) recruited by Jango Fett to disappear from the galaxy for a decade, training the Clones in the art of war in total secrecy. Naturally, the Mandalorians passed on their beliefs, and the Clones they shaped had a better chance of survival.
The question fans will ask is: what happened after the decade was up? Most of the Cuy'val Dar returned to their lives, or took on new ones. They had the freedom of anonymity... because it wasn't their face on every Clone soldier. If Jango was as famous a bounty hunter as he seemed, every Mandalorian would know that he allowed his blood, his training, his beliefs, and his culture to be mass-produced. Copied into thousands of soldiers designed to die for the Republic, and not Mandalore. If you ask us, the idea that Mandalore would disown Jango as a traitor is completely believable.
Boba Fett Became an Outlaw, Like His Father
That's our theory for why Jango Fett could have been publicly and enthusiastically exiled and disowned by every follower of the Mandalorian way. But for Boba Fett, the explanation is even simpler: he's not Mandalorian because... well, he never became one. It's safe to assume that Jango passed on some of his culture and Mandalorian ways to his "son" before being killed. But instead of taking his larger step into the Mandalorian way of life, Boba Fett took up with cutthroat bounty hunters and hired guns, instead (a childhood chronicled in Clone Wars).
If our theory is accurate--or at least based in the same expanded universe fiction the Clone Wars writers were leaving possible--Boba was probably better off finding his own set of Mandalorian armor instead of trying to recover his father's. And we suppose there is some poetry in Boba actually becoming what his father was seen as for bringing him into the world: a common bounty hunter.