Sometimes seemingly simple or obvious things are not so obvious

https://en.m.wikipedia.org/wiki/Parallel_postulate

Parallel postulate seems obvious but non-euclidian geometry does not have such an axiom. Projective geometry also has no parallel postulate requirement.

https://en.m.wikipedia.org/wiki/Axiom_of_choice

Axiom of choice in a finite world makes sense. With infinities you get the Banach-Tarski paradox

https://en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

When using mathematical precision to investigate ideas some faith is required that your axioms hold true, because alternative axiomatic systems exist that are also non contradictory. 

Think of it like axioms as defining the boundaries of a mathematical reality, and you can have different axioms that create different realities.