The main reason that we ought not use government to help the poor and the sick is that government is wasteful of that which is entrusted to them. They allow those who ought not be entitled to charity to receive it, to waste it and defraud government into giving it to them in the first place. The government wastes huge sums of money in the bueaucracy that doles out the funds.
When government gives out other peoples' money, those who received mistakenly believe that they have a RIGHT to it, not that it is in fact charity.
Private individuals do it better, more efficiently and at less cost.