I think it goes like this Eren is saying he is content with being born and doesn't think he should have never been born. Which is what the euthanization (sterilization) plan implies. Also Eren just like Grisha wants the full restoration of Eldia whereas Zeke wants Eldians to be eradicated to prevent the same mistakes from happening over again. Zeke came up with his plan when he remembered what that old Marleyan man told his parents after splashing water on them. When Eren says "because I was born into this world" he is saying his life was worth living despite the suffering. Zeke thinks that life is bad and filled with suffering mainly because of his upbringing and from understanding the Marleyan perspective of Eldians. Zeke was born to be seen as 'Eldia's hope' and the 'royal blooded savior' but not as Zeke himself. He had other philosophies ingrained into him from birth and that is part of the reason he feels he can decide for others that his philosophy is the only correct method to salvation.