1) When you climb backwards on top of an elementary school playmate on a swing. There are now 8-limbs, hence, the "spider-swing."
2) A particularly crude form of PDA, involving a couple at dinner, or any public forum, when one member drapes their legs across their partner's lap. It usually involves eskimo kissing or other acts of intimacy to heighten the level of annoyance. They are now an amorphous wrap of limbs, also, very irritating, hence, "spider-swinging."
"Your girlfriend is a serious spider-swinger."
"Sorry, I like you, but I am really not into spider-swinging."
"Dudes, quit spider-swinging, I am trying to eat."