We need a BIG because it encourages risk taking. Society is built largely on the backs of low-wage laborers, but actually benefits most from free, educated, motivated people chasing not just a living wage but a fulfilling occupation. The ingenuity of human minds is our greatest, most renewable, still hugely untapped resource. It should be society's goal to enable and tap that potential. YCombinator sort of pays smart people BIs for a summer not as a reward for work but to ENABLE them to work, to great benefit (though not entirely unconditionally, obviously). When and why have we given up hope of expanding such concepts to all of society?
We need a BIG because markets are made of people, which means there can be no free market without free people. Many people today are not free but under economic duress. Only once people's livelihoods are secured, the labor market will produce win-win situations and exploitation will be eliminated (giving everyone a benefit most of us techies already enjoy). Finally, jobs will be paid what they're actually worth to us rather than what employers can get away with. Unpopular tasks will have to be fairly (=highly) paid or automated. A BIG actually perfects capitalism, rather than undermining it.
We need a BIG because it's not possible to "live off the land" by your own labor anymore in our society. An income is required for survival.
We need a BIG because progress is eliminating (the need for) many low-wage, manual labor jobs. "Full employment" is becoming less and less necessary or desirable.
We need a BIG because many tasks society benefits from aren't paid: Caring for the elderly, raising kids,... but even writing open source software or contributing to Wikipedia. People doing such work today are either privileged, dependent on others or in precarious living conditions. All of these strike me as things we should work to avoid.
We need a BIG because it is fair and simple – paid not just to the jobless, but everyone. It is empowerment rather than a bureaucratically administered handout with all kinds of social stigma attached.