@ShelBeast As someone not connected to this - I've never set foot on the game - you may think staff owes you a detailed explanation as to why they might turn down something you want in your background or want to have access to, but the truth is they don't. It would be nice to clearly know what is expected or what the reasoning is, though, and it seems to me they made an attempt to answer that based on what @Autumn reported.
The answer was given that Cole was not the founder and owner of Halo, and while Bruce Wayne did not found Wayne Enterprises, that is a direct family connection that simply transferred to Bruce. That's a small but important detail that would be different with Cole and Halo, because presumably the Cole app is trying to justify him having control of Halo and all its assets. If staff says no, he doesn't, then he doesn't.
That is not unfair or unequal, even when you add Ted Kord and Kord Omniversal, which would be along the same lines of the Wayne example above. When it's a matter of a corporation that was not founded by the character (or character's family), or the character is simply connected to it through an association, even if comics canon leads to him eventually coming into control of it, that doesn't mean the same thing is going to happen on a game. Staff has other things to factor in there when it comes to handling multiple players and characters, and more importantly, potential players and characters.
All that said, starting this part of the thread off with a somewhat vague criticism that accuses staff of playing favorites and acting like the issue in question is trivial and an attack on you (while not giving details or even saying it was about you until more details emerged) makes it look like you're out to create drama. You are unhappy that you didn't get to have your way, and that's fine, but that doesn't mean staff is out to get you. I'm sure they're trying to keep a balance in mind when it comes to in-game corporations that go through family ownership vs. outside ownership changes.
If you stick with the character and eventually settle in, perhaps you will have the opportunity to run a plot that winds up with Cole owning Halo.