Why shouldn't we use government on poverty/social problems?
Because that's not what government is for. The purpose of government is to protect our rights. The Declaration of Independence said it best:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men
Most libertarians believe that some form of government is essential for protecting liberty. However, they also maintain that government is an inherently dangerous institution whose power must be strictly circumscribed.