Final answer:
Producer George Martin insisted that session drummer Andy White replace Ringo Starr at The Beatles' first studio session. This occurred because Martin was not satisfied with Ringo's drumming. Ringo quickly overcame this hurdle to become an integral part of the band.
Step-by-step explanation:
The individual who insisted that session drummer Andy White replace Ringo Starr during the Beatles' first studio session was producer George Martin. This decision was made because Martin was not initially impressed with Ringo's drumming during their first recording session, and as a precaution for the band's second studio session, Andy White was brought in to play drums on what would become the single version of "Love Me Do" and "P.S. I Love You". Ringo was relegated to playing the tambourine on "Love Me Do" and maracas on "P.S. I Love You" during this session.
While this decision may have initially caused some tension within the group, Ringo Starr quickly established himself as a crucial member of The Beatles, contributing significantly to the band's unique sound and success. George Martin's initial judgment was part of the band's early developmental phase and is now a footnote in the broader history of The Beatles.