Because working minimum wage is horrific and I'd rather pay a proportion of my own (minimum wage at the moment) earnings every week than see others have to go through it.
If someone earns minimum wage, just maybe they should learn new skills or find a different job or move to another part of the country? Of course there must be a safety net to help the truly needy, but I really don't see the need for a minimum wage in a free society. If I have useful skills, employers will pay what my skills deserve. If they don't, I'll find other employers or start my own business. For sure, I'm not going to sit around and ask the government to help me. If you disagree, you're more than welcome to contribute voluntarily to the income of others you know. Just don't force me to do so by law.
It's not as if most of the people claiming benefits are doing so to escape from a working market where they're respected and given the responsbility that their talents deserve.
Sorry, but that's bunkum. If employers are willing to pay someone only minimum wage, then maybe their talents are worth only minimum wage. Depending on the situation, maybe minimum wage earners should consider learning a new trade or going back to school or, in some cases, working harder. The free market comes closest to ensuring we receive what we're worth. Government regulation, such as imposing a minimum wage, is a social policy, not an employment one. In fact, the law is anti-employment because companies think hard before employing someone.
The exception, of course, is to help those who are truly in need - the physically challenged, the blind, the deaf, the mentally challenged, the chronically sick, and so on. It's also OK to help those who've been discriminated against in the past, such as women and minorities. This is a sign of a compassionate and fair society. I don't see why the exception should extend to those who simply never bothered to learn when they had the chance - although we should provide the opportunity for them to catch up when they change their mind.
(Waiting for the comments of Comrade Earl.

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PS - note to Songbird. To some extent, I'm playing devil's advocate with my response, so please don't take my words personally. You note that you are earning a minimum wage right now; maybe it's by choice and maybe it isn't. I once earned much less than the minimum wage in Britain (when you take into account train fares, etc.), but it was by choice as I learned a new profession. Income size is not the ultimate criterion of success in life, I agree, and there are times when it's right to invest our time without "adequate" compensation. In the end, though, it's not for the government to tinker with our financial destinies. That right belongs to us.