Defects, problems and incidents

Answer:
Incidents lead to problems, that's correct (see the articles
ITIL Problem Management: getting rid of problems https://advisera.com/20000academy/blog/2013/08/05/itil-problem-management-getting-rid-problems/
How to make your ITIL/ISO 20000 Problem Management more effective with a Problem Record https://advisera.com/20000academy/blog/2017/02/14/how-to-make-your-itiliso-20000-problem-management-more-effective-with-a-problem-record/

On the other side, defects relate to not satisfying service requirements and involve e.g. change on the service in early life support phase. According to ITIL, definition of a problem is " A cause of one or more incidents.". So, if that defect doesn't cause incidents, there is no need to go to problem management. It's rather that you need to send it back to development (Release and Deployment or even to Service Design processes if you conclude that there is an error in service design). So, as you could see, defect can have much deeper causes then "usual relation" incident -problem.