The bilingual brain benefits shrank when the studies got bigger
The honest version, which is still a good enough reason.
Early studies reported a strong cognitive advantage for bilinguals: better attention control, delayed dementia onset. The findings travelled fast and became a selling point.
Larger studies, and pre-registered ones, found the effect much smaller or absent. Publication bias played a part: studies finding an advantage were more likely to be published than studies finding nothing.
This site is built on corpus data and it would be dishonest to quote the shaky claim while showing the solid ones. So: the brain-training argument for learning languages is weak.
The argument that survives is the one that was always better anyway. A language gives you access to people, to what they wrote, to how they divide up experience. That is not a side benefit that needs a brain scan to justify it.