Fetching details from the dictionary...

to begin to say; to start talking; to broach (a matter); to bring up; to come out with
to be the first to say; to suggest (doing); to propose
彼が急に言い出したことに驚いた。
I was surprised by what he suddenly said.
誰が最初に言い出したのか分からない。
I don't know who said it first.
自分から言い出すのは勇気がいる。
It takes courage to bring it up yourself.