Luchar vs. combatir vs. pelear
The Spanish verbs 'luchar', 'combatir' and 'pelear' all convey the basic idea of engaging in some form of conflict but are used in slightly different contexts.
Luchar
'Luchar' tends to be used to represent the idea of striving or struggling. It can invoke a physical fight, but it often portrays a struggle related to larger social, political, or personal issues.
Nuestra organización está luchando por la igualdad de género.
(Our organization is fighting for gender equality.)
Él lucha todos los días para sobrevivir.
(He fights every day to survive.)
Combatir
'Combatir' usually has a more direct connotation of actual physical conflict or battle, often involving warfare or military action. But it can also metaphorically be used to indicate an opposition towards something.
Las fuerzas están combatiendo en el frente.
(The forces are fighting at the front.)
Estamos combinando nuevas maneras de combatir el cambio climático.
(We are finding new ways to combat climate change.)
Pelear
'Pelear' is a more colloquial term that primarily denotes a physical altercation between two individuals. Though its usage is informal, it is usually associated with small-scale disputes or fights rather than grand endeavors or struggles.
Los niños estaban peleando en la escuela.
(The children were fighting at school.)
No me gusta pelear pero tengo que defenderme.
(I don't like to fight but I have to defend myself.)
Summary
In sum, while 'luchar', 'combatir', and 'pelear' all deal with conflict or struggle, there are subtle differences. 'Luchar' tends to evoke struggle on both physical and metaphoric fronts especially for larger issues. 'Combatir' leans more towards physical warfare but can also denote a strong opposition, while 'pelear' commonly illustrates small-scale physical altercations.