What I suggest is finding a site online that lists the criteria for what are the commonly accepted symptoms for sociopathy. To define a socipath they need to fit the profile.
The person you describe sounds like they are requiring a high degree of attention from others. A teacher will have the attention of students and maybe has come to demand/expect that. When the child was born, this man loses interest, that is, he no longer has the full attention of the partner. Took possession of the child - there's a lot of anger there.
I would say that this person is reacting from strong feelings of rejection. His possessive behaviour to the partner at first is a way for him to control any feelings of rejection he might be afraid of experiencing.
Dragging the child out of the pool when the child was told to leave the pool is another indication, I think, of him feeling rejected - that is - his authority to the child is ignored, and thus his rejection feelings are triggered. He has reacted with aggression - taken the child's ignoring him as a personal affront to his self-worth.
If you know this person reasonably well, I would be looking at his own family history for more of the clues here.