Gio was abandoned by his parents and his grandma because of his condition. That's blood related. How can Felix not. I think that's why he's too afraid for Felix to go.
And stop with the he's manipulating Felix. Felix and the doctor/bff will manipulate him as well in the next chapters.
Also Leegang flashback. He's the best little brother. Sadly Gio doesn't really care about them anymore. Just like how his parents and grandma don't care about him as well.
People kept saying to talk it out when Gio is not really ready for it and on the following ch you'll really feel how not ready Gio is for all the things going on rn whether its for his real parents, his brother, addressing his sickness, and talking things out. He has trust issues because his family abandoned him and afraid that Felix would do the same. So he uses his sickness to have assurance (assurance is the right term whether for himself or for their relationship) that Felix will not abandon him as well. Then they argue and Gio being immature and said nonsense to Felix because he has trust issues. I do think he just accused Felix, not yet to the point of being manipulative. And spoilerss on the following chapters the doctor and Felix told Gio that his sickness is getting alarming and proceed to do the treatment without telling Gio. That for me is kinda sketch since its Gio's body and he should decide whether he'll do the treatment or not.