In one of the therapy sessions, Will and Sean do not speak to each other. Professor Lambeau asks Sean why he didn't say anything and Sean replies by saying that Will is the one who needs to speak first. I do not understand why Will needed to speak first. Is this something related to psychology (the actual treatment) or does this have some underlining symbolic meaning (literary).
Here's the actual script from the meeting you refer to:
INT. HALLWAY -- LATER Lambeau and Sean walk down the hallway after the session. LAMBEAU What do you mean "he didn't talk?" You sat there for an hour? SEAN No, he just sat there and counted the seconds until the session was over. It was pretty impressive, actually. LAMBEAU Why would he do that? SEAN To show me he doesn't have to talk to me if he doesn't want to. LAMBEAU Oh, what is this? Some kind of staring contest between two kids from the "old neighborhood?" SEAN I won't talk first.
This is actually, I believe, the 3rd session. The first one, Will comments about the painting and we find out about Sean's wife. The second one, Will and Sean go to the park and Sean basically calls Will out on his M.O.. That meeting ends with this monologue:
SEAN Yet you presume to know so much about me because of a painting you saw. You must know everything about me. You're an orphan, right? Will nods quietly. SEAN (cont'd) Do you think I would presume to know the first thing about who you are because I read "Oliver Twist?" And I don't buy the argument that you don't want to be here, because I think you like all the attention you're getting. Personally, I don't care. There's nothing you can tell me that I can't read somewhere else. Unless we talk about your life. But you won't do that. Maybe you're afraid of what you might say. Sean stands, SEAN (cont'd) It's up to you. And walks away.
During the 3rd meeting, Sean simply waits him out. Will has to be the one to initiate conversation, Sean already put the ball in his court.