If you want a cheap flight from Birmingham to Belo Horizonte, you've got zero airlines to choose from.
Belo Horizonte Tancredo Neves International Airport is just one of the airports in Belo Horizonte. If you're not set on a specific airport, try changing your search from Belo Horizonte Tancredo Neves International Airport to Belo Horizonte to see a broader range of flights – they might be cheaper.
If you're planning on going to Belo Horizonte during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.