I'd say that it's neither an agrument for or against a welfare state per se, but it's an argument against the welfare state being led by benefits. There will always be those who genuinely need help and benefits should always be a part of that, but the main driver should be to enable people to be employable.
I think though, that you need to take the analogy a little further:
* If you teach 100 men to fish, then give them access to a river with enough fish to feed 80 of them, then 20 of them will still be reliant on handouts of fish (There are more people unemployed than there are jobs available).
* If you teach a man to fish, but then he breaks his arm - he will need assistance until his arm heals (help is required for the sick & disabled).
* If you teach a man to fish, then poison the water - even more will be reliant upon benefits (the number of jobs available - particularly at entry level - is reducing).
A welfare state should be driven towards enabling people to get a job, but it should also bear in mind that it might not be possible. That's where benefit payments come in. I've spent all but a couple of months of my adult life in education, employment or both - but I'd rather have a benefits system that was benefits led than none at all. I'd also say that if we're going to err on one side or another - I'd rather err on the side of being too generous than too stingy. Better to pay 10 people a little more than they deserve than leave one vulnerable person without enough to live on.
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ETA: Time for heroes said, "I find that if you put (UK only) at the end of your questions you avoid a lot of the crap, partisan, one line answers that you've got here, ".
99% of the time I would agree with that statement (it's why I added "UK" to my Y!A ID) - but Krista has given an answer that's based in America, yet it applies to the UK electorate as much as it applies the the GOP across the pond.
ETA2: I agree with Confused Hal in what he says, except that I'm not sure it's all the fault of THIS government - it's been happening for decades, as long as I can remember. The number of jobs decreasing - particularly at entry level - is just one of the downsides of operating in an efficiency-led capitalist economy. It's the fault of this government, and the one before it, and the one before that....etc (plus the global economy).
What I will say though, is it gives a strong argument to say that labour's increase of the number of public sector jobs and love of quangos, was actually the *right* thing to do - since it gives people employment and transferable skills. Better that they do those jobs (ie, teaching them to fish) than have them utterly reliant on benefits.
I was not a fan of the last government - on the whole they were ruthless & draconian and I dread the day that labour are re-elected if that's what a labour government is like - but on the use of quangos and expansion of the public sector, they were right.