'We're in orbit!' Rosetta becomes first spacecraft to orbit comet

 The arguments of healing the sick or feeding the hungry are so generically "good" as to strangle any counter-argument, so I'd say they're invalid. A better argument from your side would've been "why fund this space mission when we could've funded 5 other space missions that could yield more important results?"

No sense in mixing apples and oranges, these issues you list are unrelated.

A cynical person would even say that not spending millions on ebola clinics will save billions of dollars on the famine front, given some patience.

  
Not apples and oranges.  Guns and butter.  Totally unrelated, yet very intertwined.
 
We've got a "house" where the roof leaks, the kids need shoes and jabs, the lawn is dying and the driveway washed away in the last storm.  Yet we're spending $$$ billions on more (metaphoric) cable channels.
 
And anyone believing that letting Ebola get away from us will be of benefit on the famine front, doesn't belong to the same human race I do.  Any more than the guys that hoped AIDS would solve "the gay problem".

That analogy is not very good.

First of all, it's not our house that's in disrepair. We do regularly donate to the neighbour's family, but their father decides it's better to use the money for booze and man toys.

Now our own house is not perfect. We spend too much on the alarm system, say 40% of our income. Occasionally we buy a book for learning and knowledge. Now tell me, why should I save on the few dollars spent on the books? There's no difference in the budget.

But what I really want to know is: how would a world without hunger and disease look like? How stable will it be? How do you keep populations at sustainable levels?