Support is related to Peer. Peer is related to Equivalent. Equivalent is a synonym of Equal. Equal is a synonym of Adequate. 
Shove is the opposite of Pull. Pull is related to Gravity. Gravity is a type of Attraction. Attraction is a type of Show. 
Support <--RelatedTo--> Peer <--RelatedTo--> Equivalent <--Synonym--> Equal <--Synonym--> Adequate 
Shove <--Antonym--> Pull <--RelatedTo--> Gravity --IsA--> Attraction --IsA--> Show 