If one group controlled more than half of all mining power, it could reverse its own recent payments or block certain transactions. It still could not steal your bitcoin or create extra coins.
Go deeperNodes reject invalid blocks no matter how much mining power is behind them, so attackers can't forge signatures or break the 21 million limit. Pulling it off on Bitcoin would cost an enormous amount in hardware and electricity. Waiting for more confirmations makes large payments safer against it.