Although they (and I) would prefer that CAs could just do the role of issuing certificates with the right names to the right people, Let’s Encrypt is currently obliged by the rules of the Trust Stores (without which their certificates would not be trusted in your OS or web browser) to provide some sort of protection against issuing to sites which deliver malware and suchlike.
They use the Google Safe Browsing API to do this. You will most likely find that your site is considered to be unsafe by the Google Safe Browsing system, and if you validate your control of the site you should find Google are able to explain why and maybe help you to fix it.
I hope that helps.