If it gets down to it, though she might not exactly see it that way, I think Arakawa’s main issue and what she tends to touch on and explore is that fatherhood can be very damaging with taken to it’s patriarchial extreme and her stories are aware of that.
Hachi’s dad, Shou Tucker, Father- these are by far the most shit dads she presents. Both Father and Hachi’s dad take the intimidating patriarch thing to the extreme. They deliberately shut off emotion. They command and push their children rather than show affection. They seem to believe as long as they treat their “kids” strictly and push them constantly they’re doing their duty as fathers. No need for silly feelings and hugs and shit. And it’s really hurt Hachiken and of course the homunculi all die (cept Pride). As long as they’re the breadwinner (or like, able to take over the world), they don’t have to be there for their family either
Shou Tucker doesn’t seem to feel any emotions or affections either, and but bread-winning SO ABOVE everything else that he destroyed his family just to bring in more money for the household.
The “absent” example was Hohenheim and where he fucked up was actually not expressing his emotions to his children when he left. They only start to get a little closer when Ed and Al see Hoho’s emotional, affectionate side.
And Hughes, the good dad, is openly affectionate and emotional.
Motherhood is always framed as inherently emotional and affectionate in society, and Arakawa sees that as a good thing for children, but I think she thinks of society’s ideal of fatherhood is flawed and can be dangerous, and sort of explores that in her own way. I guess!