How did Mexico loose Florida?

Answer 1

It didn't. When present-day Mexico was still a part of the Spanish Empire and the United States was still a colony of the British Empire, Spain ceded the Florida Peninsula to England according to the Treaty of Paris, in 1763.

Answer 2

Texians wanted to keep Texas as a slave state.

First on the background of the war:

When Mexico won its independence from Spain in 1821, all the territories it possessed included Mexico, most of Central America (Guatemala, El Salvador, Honduras, Nicaragua and Costa Rica) as well as today's US States of California, Nevada, Utah, Texas, Arizona, New Mexico and parts of Colorado, Oklahoma, Kansas and Wyoming.

Due to the extremely low population for such territorial extension (estimated at 12 million during 1824), Mexico relaxed its Immigration policies, thus allowing American settlers to help populate the northern territories. The conditions to settle were simple: 1) to pledge allegiance to Mexico and 2) observe the Mexican Law and customs. In 1830, these laws incorporated the banning of slavery. Due to the fact that many American settlers in such territories were slave owners, they looked for any pretext to break up with Mexico.

Later, Mexican President Antonio Lopez de Santa Anna took measures to transform Mexico from a Federal Republic to a Centralist Republic. This move prompted Yucatan and Texas to secede from Mexico. Santa Anna's government invaded both republics; while Yucatan was regained, Texas was lost. The Texas Revolution ended after the Battle of San Jacinto, but Mexico did not officially recognize the independence of Texas until after the Mexican-American War (1846-1848) as part of the Guadalupe-Hidalgo treaty.