godan verb (-su), transitive verb
begin to say; start talking; broach; bring up
Used when someone initiates speech or introduces a topic, often a difficult or important one. The object is typically the matter being brought up, marked with を.
彼は会議で新しい提案を言い出した。
He brought up a new proposal at the meeting.
She suddenly said she would quit.
godan verb (-su), transitive verb
be the first to say; suggest; propose
Emphasizes being the initiator of an idea or suggestion, often in a group context. Common with ～しよう (volitional form) to propose doing something.
誰も行きたがらなかったが、彼が最初に行こうと言い出した。
No one wanted to go, but he was the first to suggest going.
彼女がパーティーを開こうと言い出した。
She proposed having a party.