It's not a dumb question!
It's basically a mess of poor impulse control, a little OOC stuff, which was discussed in Discord, and via PMs, and ultimately that Izzy and Takeda are more loyal to each other then the Prince. They were not happy about bonding to the Prince, but accepted it, so they could have their bound. Then it was a cultural thing, Ale didn't want to do Takeda's plan for the hunters, which felt like a slight against her honour, and a sign that there was no trust, even though Alessandra made Takeda her Reeve. Which Izzy wouldn't let stand, she's sworn herself to Takeda, and yes she means first. She has waited years, centuries even to serve the Takeda Clan again so finally finding one and remaining loyal to her is more important to a Prince and to a Domain that the haven't been loyal too for very long. There's always more Domains and more Princes.
What called for Initiative was that the Prince wants to remove Takeda's sword hand. Which is a big not going to happen for Izzy and Takeda. In Izzy's point of view, it would be kinder to simply demand Takeda's death, instead of forcing this dishonour.
I'm actually in awe over how Orianna's been handling Ale as Prince, it's epic. And if I was playing any other character I would be bowing down and trying not to pee myself!
But I am not playing another character, so I'm being as true to Izayoi Goto as I possibly can be, and while yes the direction of In Service was discussed OOC, nothing was said by anyone that lead to a big fat 'NO! Let's think of a new way to handle this'
So it is what it is.