My ex-boyfriend is someone who induces people to believe that I was the one who first told him that I like him.
He wants to say that he has never declared his love for anyone yet.
He's a scum who just wants to show off.
ご質問ありがとうございます。
"My ex-boyfriend is someone who induces people to believe"=「私の元カレは人々に信じさせるように仕向けます」
"that I was the one who first told him that I like him."=「私が彼に告白したと。」
"He wants to say that he has never declared his love for anyone yet."=「彼は誰にも今まで告白していないと言いたいのです。」
"He's a scum who just wants to show off."=「彼は単に自慢したいクズです。」
ご参考になると幸いです。