Birds don't fly south for the winter, Canadians do. The birds fly North for the summer and I bet you think that's the same thing! :-)
If you look at this properly, you'll discover something you didn't know about migration. Birds we see in Belize, (Neotropicals) have been moving north slowly each season and retreating a little less south since the end of the ice age.
The American continent was very different during this frozen era. Most living things where compacted into areas near the equator.
The ancestors of neotropical migrants originated in Amazonia (an area believed to be 15 million years old, known today as Brazil). Areas north of this were not at that time in the earth's history temperate enough to reside in. Amazionia was then and today the greatest expression of life on the planet. One third of the world's birds still live there. As the ice age ended, areas to the north of Amazonia were habitable during summer months and provided refuge from competition for food and shelter in this over-populated area. But in winter months migrants were forced to retreat. Each year as the ice receded, more northern territory became available as refuge during summer months and migration distances increased. As some found the decreasing winter months tolerable they became residents in places like Belize. Canadians go home in spring and birds migrate north. Does that seem like a 'same difference' still? I said you where going to learn something new."