Kuta who had not yet figured out had been disowned and replaced but also had even an assassination attempt made on her. All of this is done by not just her own family but her father mind you. So rather than accept the knowledge that she had probably been betrayed by her family just now and then move on from there. Kuta was clinging to the hope that none of this was true and that it was all just some lie. That this was some setup being done by someone looking to frame her family or somehow use this as blackmail. Something to clear their name and make so they were not the ones behind this at least her direct family. And so she just kept heading back to where her family manor to get that proof from them directly. She did not go back to the place where she was staying at the moment because she did not trust going back there.
Thinking this was a scheme set up to frame her family going back the way she came to it. That would seemingly be playing into their hand as she did not want to get into any fights that she did not have to after all. She just wanted answers instead thus, she was going to deal with the issue at hand as fast as she could. Getting slowed down by going back to the very place she had been. That was not part of her objective at the moment as she had nothing there she really wanted to go back for in the first place. She had everything she needed on her already and that was probably in case she accepted the servant's offer. However, the one thing that she had brought with her that she dumped here was the sword she was given as she was not going to use it and/or need it at any time. So just leaving it was getting rid of what would otherwise just be considered deadweight she was unnecessarily carrying with her.
As for the servant that attempted to assassinate her just now. They were not expected back either given they were considered a loose end that would be dealt with one way or another. They wanted to give Kuta one last chance to 'right' the wrong she had been revealed to have made and start over on the path to the sword truly. They offered her more of a final chance than her own parents were to her. However, she rejected it and thus the servant died trying to kill her thinking she could not properly fight them back in her current state. While the Sabres were not worried if Kuta survived as no one would believe her claims after all. Her very existence as a mage would discredit any claims she could make to being Kuta Sabre anymore. To them, she was now a girl with the same name as the family head's daughter. They were also silencing a servant who did not seem loyal to the Sabre family bloodline but instead picked a single member or the entire family as a whole.
Kuta was an anomaly that appeared within the family. One that had to be dealt with immediately to ensure that she did not spread it further to any other members. Anyone who did not want to accept that fact they were also considered to be something that needed dealing with at once. Thus the servant was also removed from their own family as they cut all ties with them to protect themselves. Claiming their actions were not those of the family but their own individual ones that they were taking without their family's consent. Thus both Kuta and the servant were abandoned yet one went to their grave unaware of this fact while Kuta herself was still very much alive to see it for herself.
She would not even learn this from a member of her former family directly but instead, the movement that could be considered a usage and/or abuse of the power and influence the Sabre name possessed. When Kuta made it back to the city where her family manor was located, she found a flyer claiming that the youngest swordmaster in history would finally be given their official title. This after an incident that left them recovering that happened on their birthday thus the reasoning why she was doing anything recently.
'But I already have a title as everyone calls me Spellblade so that is my title as swordmaster, right' Kuta thought.
Unaware that her current title was indeed unofficial as that was just a nickname that was given to her and should she not have been revealed as a mage. Then it might have become her official title going forward. However, that was no longer the case as her former father had changed the title to something else and was now calling her replacement something else entirely instead(Kuta herself was still unaware of all this).
Kuta held the flyer in her hands as the image staring back at her was indeed of herself to a degree that was shockingly so. If this had happened before her birthday then she would have wondered just when was the picture taken without her knowledge. The person in the picture looked that much like her but they could not be her though. This was a recent one and looking at herself she knew that this person could not be her as she was now, just as she was before she woke up on her birthday. It also claims they would be making their first public appearance in years. Sure she had isolated herself for the last few years but that was just to truly perfect her sword style for the weapon user school. She just did not want to mess up as this would be the first time she be primarily around others her own age even if they were not exactly at her skill level. Thus the reason to train is to use her full power at whatever level she would need to. Not holding back but fighting everyone at their level or close to it.
Kuta was not aware of just how abnormal this was and even more how she actually managed to pull it off. Able to fight someone at her best without overpowering or overwhelming them because of the skill and experience gap. She could provide anyone with a challenge that was almost as if it were tailored to their abilities and skills. Unaware Kuta was that trying to accomplish this in a way could be considered an insult to anyone she used this on. She was so far above them she finely controlled her powers and skills to their level. Not only that but always fights her strongest at that level as if it were second nature.