I figured people would not react well to this chapter. It's very... Japanese. XD The anime was pretty much the same, perhaps a bit worse because of the hurried pacing.
I don't agree with Yoshida at all. Sometimes the parent is stripped of their rights and responsibilities because they are deemed unfit to hold them. Sometimes adoptive parents get those rights and responsibilities in their stead. Blood might be thicker than water, but it's not the be-all and end-all of everything. That being said, Yoshida has this fixation on "just being a stranger" in Sayu's family situation, so him saying this doesn't really surprise me.
And on the other hand, what Yoshida (and then Sayu's brother) does is quite a slap in the face for Sayu's mother, in a very roundabout, Japanese way. We may have become desensitized because of how often we see it in anime (especially in comedies), but the dogeza is serious business. Yoshida humiliates himself in front of her to the extent that she simply cannot say no, especially with her son joining in, and especially when Yoshida's request is something that everyone in the room knows should be her friggin' obligation as a parent. With this, she can no longer hide behind her rants about how much she has suffered blah-blah-blah. Yoshida pushed the envelope to the point that it no longer matters. No wonder she snaps (again).