I don't disagree with libertarianism as a broad general policy. Governments do sometimes overstep and become intrusive — just look at the American Revolution. People do need to be reminded that government is sometimes a problem. Where many† libertarians go too far is to assume that government is always a problem.
My main problem with strict libertarianism is that it refuses to acknowledge that structural inequalities exist or that they need to be addressed. Structural inequalities and market failures can only be solved at the group level (for example: discrimination , monopoly distortion , and environmental externalities).
Links that go into more detail about how libertarian policies are problematic:
If you agree with me, here's some links you might like:
† Note: There are many different flavors of libertarianism    and I don't want to misrepresent it as being monolithic. Depending on how you define it, up to 59 percent of Americans identify as libertarian. I don't have a problem with the looser versions of libertarianism, it's only the stricter ones that I have issue with, ones that are closer to minarchism.