"The MAN who gave himself" is the particular point here--the anointed Jesus, who finished the giving of himself at Calvary, is the "Mediator between God and men."
It was the “Man” (Greek, Anthropos, the human being, the Messiah (Savior) Jesus who by means of the ransom sacrifice became the mediator between God and men.
"The man Christ Jesus gave himself a ransom (anti-Lutron: corresponding price) for all, to be testified in due time." (1 Tim. 2:6)
Our Lord's offering of himself as a sin-offering and corresponding price for Adam was a complete settlement toward God for the sin of Adam and all those who lost life in him. Jesus, by the payment of the penalty upon Adam, gained the legal right to restore both him and his posterity to life.
"As by a man (Adam) came death, so also by a man (the man Christ Jesus) comes the resurrection of the dead." (1 Cor. 15:21)
The philosophy of the ransom is that all mankind were included in one man's sentence, to the intent that in due time the penalty of sin could be paid for by the one sacrifice.
A perfect man had sinned. Only a perfect man could pay the price. Only a tested, proven, perfect man could be the world's ransom-price.