Earnest : The RSV reads "... to care for the church of God which he obtained with the blood of his own Son" with a footnote "Greek with the blood of his Own or with his own blood".
aqwsed12345 : The RSV appeared in 1952 with the literal wording “with his own blood”; the wording you quote is the 1971 “Common Bible” revision produced for ecumenical use and reprinted in the NRSV family.
This is just to report back that I checked the 1952 RSV and it does read "with his own blood" but it has a footnote "with the blood of his Own" showing that even back then they recognised there were two ways of translating this verse. No one (except Hort) has claimed that the word "son" stood in the original, although Metzger does say that palaeographically such an omission would have been easy.
The claim is, as the NET bible explains, that the genitive construction could be taken in two ways: (1) as an attributive genitive (second attributive position) meaning “his own blood”; or (2) as a possessive genitive, “with the blood of his own.” In this case the referent is the Son, and the referent has been specified in the translation for clarity.
You keep on insisting it can only be translated in one way i.e. "his own blood", but many translations either translate it differently or record alternatives. Most translators will translate in a way they think is in harmony with the rest of scripture which is why so many translate it as "with the blood of his own Son".