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When climbing straight and level all of the lift generated by the wings points straight up, i.e. 100% of lift is getting us higher and further away from the ground. Turning an aircraft requires it to bank or roll in the direction of the turn. Some of the wings lift is now used to make the turn rather than climb.
This means that turns on the departure track cause the aircraft to climb slower and keep them closer to the ground for longer. The result is more noise, closer to more people for longer. Closer to the ground also gives the pilots less time to react to an engine failure.
Flight Club has a YouTube video explaining how aircraft turn with nifty graphics that make this clearer.