Most of the reason for having an agent and not doing it yourself is to have the agent act as a buffer from having to hear the team argue why they don't believe you deserve that money and try to minimize some of what you accomplished or explain it away...
No matter how good the intentions are between the two sides, a player hearing this will always have some level of hurt feelings whereas he would not be privy to all the details and things that were said between the team and agent and the agent would soften whatever negative stuff was said plus he would be hearing it secondhand.
This is the biggest issue with players trying to negotiate for themselves. They hear stuff they can never unhear from the team and they are human, it is going to effect their attitude and feelings towards the team in a negative manner.