> "Many" does not necessary include "most" but "most" does include "many".
No, it doesn't. If a set is of sufficiently low cardinality, “most” (in extreme cases, even “all”) of the set may not be “many”.
Most-all, in fact—Catholic Presidents of the United States have been Democrats. But it is not the case that many Catholic Presidents have been Democrats.
Most women to have served on the US Supreme Court did so only after its first 200 years. But, again, there were not many women who served on the Supreme Court only after its first 200 years.
They said "Most other countries" and you replied with "Many countries"
"Many" does not necessary include "most" but "most" does include "many".