“The way of fools seems right to them, but the wise listen to advice.” People just think they’re right. Look also at Isa. 10.13. Obviously a person wouldn’t hold to a position that he or she knows to be false. They think that what they believe—whatever it is—is right. People are often just too full of their own opinions and not open to the wisdom of others.
But here is what the proverb is about: The wise are not convinced that their way is invariably correct, so they are willing to pay attention to advice that they gather along the way. The wise person has an opinion without thinking he/she is right all the time, and is open to listening to others, considering other input, revising his position or opinion, and continually learning and changing.