Is it a bad sign when your boyfriend walks with you with his hand on your butt in public but he will not hold your hand or have his arm around you?

Oh, dude, that's a red flag bigger than a matador's cape! If he's more interested in your butt than holding your hand, it's like he's treating you like a piece of meat on display. You deserve someone who values you for more than just your bootyliciousness. Time to kick that disrespectful behavior to the curb!