What's the opposite of sensible?

Insanity

"Foolish"

Stubborn.

Not sensible

Unreasonable

Sensible can be used interchangeably with reasonable, in today's English, though initially sensible meant having feelings, such as empathy, compassion, decency. However, it can mean both things. For example, Jane Austen's novel Sense and Sensibility was a lovely antithesis, sense being intelligence, and sensibility being feelings, i.e., it's all about the struggle between the heart and the mind.

Frivolous