I know you said not to worry about sizes and such, but a mismatch in threading *is* a possibility. Most recent bikes with threaded bottom brackets use English threading (1.37 inch, 24 threads per inch), but there are other standards out there. If you've got an older bike -- especially if it's French, Italian, or a Raleigh -- then there's a good chance a common English-threaded bottom bracket won't fit.

...but if that's not the issue, sometimes it's just a tight fit. The last bottom bracket I installed wouldn't thread in easily by hand. It went on smoothly without excessive wrench force, though.