If the Tumbler in the drivers side has a problem, it could arm the alarm but not disarm it.
Whenever you lock the car with the key, it will arm the factory alarm.
You should have your Drivers side tumbler looked at and replaced if necessary.
P.S. I'm not a tech, but I read Benzmac's Advice, and It sounds to me like he is right about the tumbler.
'92 300CE - Sold
2004 C240 - C7 Wheels
2015 ML350 - P1, Pano, Ash poplar wood, Sport Dinamica interior, Running Boards Keyless go.