to teach fishing, not to give fish. Namely, government should provide assistance to poor people so that they can work to earn their bread. For example, lowering income tax can encourage people to work.
Government takes money from people and spends it on people. Although "taking less" from people seems to be similar to "giving more" mathematically, it is quite different. One encourages people to work, the other rewards laziness. (There is an exception. Namely, for disable and elderly people who cannot work physically, government can only give cash aid. But the amount should be quite limited.)
Now, let's talk about the milk. To help those kids in mountain village, the government should not give them free milk because it gives the wrong message. Namely, you do not need to do anything to get award. Instead, the government can build a road to the village or provide free school bus. The government can lower taxes to any parents who stay in the village to care their kids.
The bottomline is to motivate people to work and enourage people to produce more. Minimizing government involvement tends to reduce waste. But it is a long story and I will not discuss it here.