How could Sheikh Al-Albani have overlooked the great scholars who preceded him, who did not deem weak the hadiths that he did, even though they were more knowledgeable than him and closer to the Hadith?

The rulings of authenticity (sahih) and weakness (da'if) on hadiths are matters of ijtihad (independent reasoning) about which scholars differ. The correct view may be with the one who authenticated the hadith or the one who weakened it. No scholar is infallible, and a later scholar may correct an earlier one. Everyone's statements can be taken or rejected. If Sheikh Al-Albani differed with those who preceded him in their ruling on a hadith, the correct view might be with him. One who is proficient in the science of hadith may perform tarjih (weighing and preferring one opinion), otherwise, one should follow a trustworthy scholar.