into the 3/8" hole I drilled why?
A: Unfortunately that isn't uncommon. Dowels are often only a close approximation rather than exact size. If they have to be exact you can make your own on a lathe, or with a tool such as this dowel and tenon cutter available from Lee Valley Tools.
You can also look into other sources for dowels that are actually sized correctly. I can’t give you any particular brand off hand, but I’m sure there are some out there.
As an aside, here is a fun article on miniature turning if you want to get excessive about things.