I think it goes deeper than this. Having watched the film with my summer stock group, we had a very long conversation on this topic.
Keating's job was to make these boys the future men of their society. The men needed to find their own voices. In Neil's case; Neil discovers that not merely his dream but his personal fulfillment comes from the theatre.
This can run harshly counter in the 50's to a business man who is spending his money to see his son also become a leader. Theatre didn't represent that in the time period on any level.
Personally, the use of Puck in Midsummer is a fantastic allegory for this as Puck was a character who walked in several worlds and was master of none of them though in his guile he would often influence all of them. There is a wonderful research topic in theatre: "Puck vs. Oberon: Who's in control"
Likewise, Neil walks in many circles of which he is not afforded the right to take control... Most importantly: "His own destiny"
Keating does open Pandora's box. But that is what he's supposed to be doing. Opening the boys to commanding their own futures. Unfortunately, Keating forgets that the boys will not always be permitted to seize their own destinies because their parents may not let go of the plans they have for their children.
Honestly, and it pains me to say... Neil is the one to blame for his own suicide. The act is taken on several levels at several times but it comes down to his father's challenge. His father says, "You will not have Theatre." It is Neil who must now challenge his father and become his own person. This is by no means an easy challenge. It is obvious that his father holds a very powerful place in his heart even if it is done so thru fear and domination.
Neil must chose between the connection he holds to his father and the expectations that his father will place on him and the choice of something that truly fulfills him not merely on an experiential level but on one that gives him spiritual joy as well.
Neil choses (as is normal for the time) to abandon that joy in himself. In acquiescing to his father at that point he choses the world he will walk in. Effectively killing his heart and passion. He spiritually commits suicide.
The physical act is merely the clarifications that he does not wish to walk around life as a man already dead.
Who draws the ethical gun? Neil is the one told to make the decision and Neil is the one who can not release the limitations placed around him to be free. He could run away and sever all contact with family and be free to pursue theatre. No one person puts Neil in the situation and I think all carry some of the blame to not help him with the decision. But inevitably, it is Neil who makes the decisions of which way he will go.