Unlike political parties, it is easy to see why anarchists (who are not interested in leveraging these shortcomings for our own advantage) reject democracy entirely.
The following two paragraphs are the introduction to An Anarchist Critique Of Democracy. You can read the whole thing at the link at the bottom.
We decided to compile this critique of democracy because we recognize an inherent tension between democracy and the freedom of individuals to create their own lives as they see fit. Some of the problems we find with democracy have been acknowledged by defenders of democracy as well, but have only led to the development of amended types of democracies (as various thinkers tried to prune the concept into an acceptable shape). By contrast, our analysis has led us to abandon the concept all together, because we find some fundamental faults with the idea itself that can not be reconciled by new modifications or reforms. Our critique is of democracy in all its various forms, whether representative or direct. We are not echoing confused cries for more democracy, we are calling for its entire abolition.
...we'll investigate the concept of alienation and how democracy promotes it. We'll question the logic of decontextualized decision making, the reduction of ideas to opinions, and the near-universal acceptance of "majority rule." We'll also go over a few immanent critiques of democracy involving demagoguery, lobbying, and corruption that are more readily accepted even by defenders of democracy, and then we'll talk about why democracy is so good at maintaining and reproducing itself.
Check Your Premises