I noticed how Lucifer and Micheal were clinging to Chuck and how Raphael was reaching out to him. Is being kind of possessive and protective of the care taker an arch angel thing because Gabriel never seemed that possessive or protective of Sam?
Partially, yes! Archangels are Hideously Protective in their own right, but Chuck is even more of a special case. Virtually all angels feel the need to be close to him, earn his approval and are generally completely at ease with him.
Gabe and Cas also have this with him, but it’s more muted. They’ve already made their choices, haven’t they, and they have the Bestest Caretakers/Humans Ever, So There. Gabe is also pretty possessive of Sam, but he tends to be a bit more sneaky about it because Sam gets kinda uneasy when his cute fledgling starts snarling at perfectly nice people for daring to shake Sam’s hand. hah.
So, taking the intrinsic protective/possessive streak all Archangels have into account, and coupling it with Chuck being Angel-catnip, makes for a seriously clingy/hovering Archangel-squad ♥