Oxford: Not guided by or based on good sense.
Merriam-Webster: Not governed by or acting according to reason.
Cambridge: Not based on or using good judgement.
Collins: Not rational.
No matter what definition you read, the meaning is clear; to be unreasonable defies logic and draws attention.
For example, identify a few historical figures who were labeled "unreasonable". People like Steve Jobs, Jeff Bezos, Walt Disney, Mother Teresa, and Dr. Martin Luther King, Jr. were completely ordinary people who stand out because they refused to conform to popular logic and held strongly to their convictions. They started brands and movements that have changed the world because they insisted on being unreasonable.
It is unreasonable to build a device for a market that didn't yet exist.
Unreasonable to create an online only book store.
Insist on true-to-life animatronics in the Tiki Room complete with blinking and breathing.
Care for a population of outcasts.
Believe in a world of freedoms that had been withheld for centuries.
Being unreasonable is to believe so strongly that an idea becomes reality.
Warning: There will be critics. There will be nay-sayers. There will be those who call you irrational. If you're lucky, they will call you unreasonable.