As I understand it, only about 60% of the population is eligible to donate blood, and that percentage is falling.
For example, anyone who has visited Great Britain between 1980 and 1996 cannot give blood, nor can those who have gotten tattoos.
Probably the reason you were told you could not give blood is that you were thought to have visited a malaria endemmic area.
Unfortunately, not all American Red Cross workers or other blood donation centers are up on all of the facts about areas outside the U.S.
For example, recently I have heard of people who visited Playa del Carmen and Cozumel being turned down because they had supposedly been in a malaria area.
While malaria is present in Belize, outside of remote bush areas especially in the south, most sophisticated medical people would probably not call it a malaria endemic area. I'd urge you to go back to your blood donation center and discuss with someone of authority whether in fact the specific area you visited was sufficient to keep you from donating.