Liberty

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

Breathe Free

Why have we instituted government? To secure our rights. That is the primary purpose of government. We have a big statue that says the same thing.

We don’t care if you are tired, but don’t come here yearning a bed.

We don’t care if you are poor, but don’t come here yearning money.

We don’t care if you are among the huddled masses, but don’t come here yearning social status.

We can’t promise you any of those things. However, if you are yearning to breathe free then welcome to America.

The reason we have a statue of liberty instead of a statue of entitlement, is because the promise of America is free-dom, not free stuff.

Minarchism

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.