How do you fail at using a knife and fork? Unlike chopsticks there isn't really any mechanical finesse to it, the only learning curve is so that you don't hurt yourself on the blade if you're using a sharp knife. Kids chopsticks exist because chopsticks are hard to use, kids knives and forks exist just so they won't hurt themselves.
you could make an argument that for someone that isn't as weak as a child, getting the hang of the force needed for a knife, and to not end up with it sliding out of control from too much force is a challenge. Realistically speaking, it's not unbelievable that, the same way westerners may have a hard time with choptsticks even well into adulthood, a knife and fork may very well be hard for an adult that spent their entire lives on choptsticks.
On the chapter itself, I'm inclined to think that the offer isn't made from malicious intent, seeing as she admired her father so much, but it's certainly uncharacteristic that someone so experienced would fail to see how that could sound like even if her intentions with the proposal are good, to take care of someone she could likely see a younger, inexperienced version of herself in and likely want to repay a perceived debt to Izutsu-dad. Not to mention the whole angle from Reina's point of view, where she feels like she needs to see the company thrive to honor her father's memory, how will she see that proposal?
Honestly very curious to see where it goes from here