I had emailed a professor for a summer internship opportunity. He had accepted me and aksed me write a proposal for applying through a fellowship.
I replied back putting down some points for my proposal. I got no reply from his side. I emailed him again after 2 days and continued to do so for the next 3 weeks. Afterwards, due to no response, I believed he was not interested in me due to no email response and stopped mailing.
But now, after the deadline is over, I found out from another source that he was not happy with my behaviour for not applying for the fellowship.
How do I convince him that this was a honest mistake and I did not intend to be rude and am still interested in working under his guidance?