This post states that se is a prefix that means "without". Wiktionary coincides on that regarding the Latin word securus, which is described as a compound between se and cura, "without care". Some of the meanings include "careless, negligent", which make sense. I am particularly interested in the meaning "free from danger, safe, secure". In effect, the English word "security" (Spanish seguridad, etc) comes from securitas, which comes from securus.
What I don't get is in what sense "security" is related to "without care". Is it because when something is secure, it does not need care? Seems a contradiction to me, since security might emerge precisely because we have taken care of something. That is, security is the outcome of care.