Other answers give technical reasons why two people can come to different decisions regarding the same issue. I once read an excellent "common sense" explanation which helped me.
A school leadership team discusses whether or not to expel a student
from school for misbehavior. One group argues that learning is
negatively impacted by the student's behavior, that expelling him is
required to preserve the other students and that nothing else they
tried has worked.
The other group argues that one should give the kid another chance,
that he will never find another school and that expelling him is the
best way to ruin his future.
Both are valid lines of thought. Both represent different philosophies about life and education. Both are "right" in many ways and "wrong" in some ways.
At the end the school principal will take a decision. But that decision doesn't mean the other line of reasoning is faulty. However in the real world one needs to move forward and he can only pick one path.
Such is different paths in halacha. They might represent different philosophies, or apply to different circumstances, or different times. Picking one path doesn't invalidate the other one. Elu v'elu divrei elokim chayim.