The Short Version
The claim overstates the scientific consensus. The most authoritative sources — including the US EPA, Woods Hole Oceanographic Institution, National Geographic, and World Ocean Review — describe phytoplankton's oxygen contribution as "about half" or "roughly equal" to land plants, not a clear majority. While some estimates range as high as 50–85%, the dominant scientific framing is approximate parity (~50/50), making the word "majority" an overstatement of what the evidence reliably supports.