What causes covid-19 breakthrough infections? if you have antibodies do you have immunity?

COVID-19 infections are possible with antibody presence from prior infection of post-vaccination with current vaccines. Severe complications are usually rare with antibodies, but complete "immunity" is not always conferred by either a vaccine or prior documented COVID infection. It has not been determined how long even partial immunity is present.

Exposure to enough viral particles can overwhelm your system and cause an infection. The best thing about the COVID vaccines is not that they prevent people from getting COVID (which is a great benefit for most), but that they essentially eliminate severe disease and COVID-related deaths. So the vaccine turns COVID from a potentially lethal disease to a common cold.