Every person I've met seems to have a reason for being a libertarian. Whether it's an ethical theory they subscribe to, an economic or legal argument, a personal experience, a gut feeling, or some mix. What is your why for supporting liberal ideas?
Personally, it's a mix of my own religious/ethical feelings on how we ought to treat and respect others, mixed with Hayekian arguments surrounding epistemics and knowledge. I think we owe other people a level of respect and humility that the vast majority of governmental systems are incompatible with. In addition, I feel liberalism (or libertarianism if you want to use that word) is the only system that actually has faith in people's capacity for goodness and ingenuity. Coercion and modern states generally are an insult to everything that makes human beings incredible