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Someone has already introduced the topic, but I want to delve deeper and give my vision on the matter.
This is the kind of thing that, when you think about it, is so obvious that you can't help but feel a little silly for not noticing it sooner.
When we talk about cooking, the doors are opened for many interpretations, but we will not go to something as complicated as… analyzing the dishes that appear next to the names of the episodes. It's something much simpler.
Cooking is something that we can associate with independence and maturity. I think this is easily represented by Arajin's mother, who, although she can be somewhat eccentric at times, let's not forget that she is also the owner of her own restaurant, in addition to having to take care of her son practically alone (as far as we know) both being responsibilities that are not exactly easy to carry. We even have Arajin himself, who despite demonstrating questionable behavior throughout the story, we know that he helps his mother, again, a responsibility about which he usually doesn't complain, being one of the few things that probably helped him with his trauma and develop a skill necessary for adult life, or in his particular case, a business that he will most likely inherit.
We can talk about the scene in which Arajin and Matakara cook together, these are already my conjectures, but perhaps it is a way to contrast how each one has tried to cope with their lives, and it's even more revealing if we remember that they were making gyozas ( They are stuffed/external part, internal part), showing us that Arajin (despite what one might think) has had more tools at his disposal (which his mother also provided him) to move forward than Matakara, who has managed to do so, as we can see, with great difficulty.
Akutaro is another one we see cooking in episode 7, but since it's something he's doing more out of obligation (and possibly threat) perhaps it's more to emphasize that HE NEEDS INDEPENDENCE (he depends on Ichiya) and learning to manage with his own resources to mature.
Now let's talk about what really matters, cooking and love. Cooking has an important relationship with love, being very commonly represented as one of the most sincere gestures of affection, both for those who cook and those who eat. Let's remember when Marito is hospitalized and Mahoro visits him, the food that she prepares for him is well… we know… peculiar, but we see that despite this, even if it's not in front of his sister, Marito makes the effort to eat what she prepared for him, making us understand that despite seeming distant, he appreciates her.
On the other hand we see it in Arajin's mother and the effort she puts into preparing his lunches for school.
We also notice it with Matakara while he prepares the party to welcome his brother, where he offers to help Arajin to make the food. Let's remember that the only person with whom we have seen Matakara cook apart from Arajin is his brother, therefore, the two people for whom he feels the most affection. That's why he wants Mitsukini to eat something that he prepared with his own hands.
But here there is something else. We talk about cooking as a sign of maturity and affection for those we love, but there is something else, and you should already imagine what I mean. Cooking as a representation of a home and its warmth. We already see it with all of the above, especially Arajin, who if there is something he doesn't lack is his mother's love and support . Personally, this makes Matakara's situation even sadder, because if we are good observers, we have NEVER seen Matakara eating or cooking with his "relatives." Basically yelling at us that he doesn't feel part of them, which is confirmed when he simply leaves after what happens with his brother.
In contrast, Arajin's house is a place where we know that beyond being also a restaurant, it's a place where cooking is done with love, therefore,it's not just a house, it's a home.
And now that we know about his past, it's just heartbreaking. Deep down, Matakara not only wants strength, he wants someone who won't abandon him, he wants a home and feel its warmth, maybe that's why we see him so happy making gyoza with Arajin, because it had been a long time since he could experience it. In the end, for Matakara, any place where he can be with a person he loves is his home.