Don't insecurities arise from self hate? For example if we are insecure about our face aren't we hating our face - hating ourselves?
Self-hating and insecurity are not the same.
Self-hatred or self-loathing is an attitude in which one thinks he/she is not good as a person from various reasons and does not accept and love him/herself. No matter what the cause, at some point one needs to realize that self-hatred is a conscious attitude, so a decision.
Insecurity means that one is not confident about a certain personal characteristic or capability, which can make him/her anxious, but not necessary self-loathing. One can be insecure but still love and accept himself.
In summary, insecurity is a feeling one may not be able to overcome at times, while self-hatred is an attitude that can be changed.
Experiencing and accepting love from others can help one to start love him/herself and to be more secure.