A connecting flight is necessary. Belize has no international airline of its own. Like here in the DR, occasionally a carrier pops up offering flights to destinations outside Belize usually to Cancun or Panama, but these don't seem to last long. A few US airlines have flights from Texas and Miami and during the tourist season, sometimes limited charter flights are available. I cannot think of a single day when there would be 200+ people wishing to fly to Belize so being able to fill a plane is not likely very often.
From outside the US, you'll need to get closer to Belize where a regional carrier can take you the rest of the way. Usually expensive. An alternative is to fly to Cancun and take the bus to the border town of Chetumal. Similar to taking the bus from the north coast of the DR to Santo Domingo.
Belize for the most part still is a very third world country. Lots of official corruption, a high rate of violent crime, a poor population, poor roads, atrocious internet access, unreliable infrastructure and as already mentioned, lots of animals that, can do you in or at least make you very miserable. Quality healthcare is a problem so most foreigners opt to go to Mexico for treatment.
One plus, Belize is not an island so getting out of there for a few days or to go buy stuff in Mexico is not as big a hassle as here in the DR.