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So that they wouldn't object to his decision. The poor thing was on the verge of suicide. Angel wanted Connor to have a feel of a normal life rather than to be a product of Holtz and Jasmine manipulations. Angel wanted what he knew was best for Connor. He didn't want to hear of any arguing of his decision.
Angel could see the team as a threat to Connor's future happiness. Wesley has already kidnapped him once, what if another prophecy appeared or something happened to Angel and thought Connor should know or be able to help, one of them could easily find Connor and tell him who he really was. Angel couldn't allow that. I also think there is an element of Angel's natural need to control those around him and be the one making the decisions.
Because he wanted Conor to have a ‘normal’ human life and for all associations with the supernatural side removed. If any of the team know about his son’s existence there could be problems down the road in some way so it is important that no one knows of his existence except Angel himself