the physical left and right hands

In a dilemma; caught between two difficult alternatives or having difficulty making a choice.

to benefit from both sides; to maneuver skillfully in social or political situations for personal gain

to shoot from both sides; to use both hands simultaneously or display versatility

to digress from the topic of discussion

caught in a difficult situation where any choice made is problematic; between a rock and a hard place

a sequence of left and right hook punches in boxing; colloquially known as the old one-two

able to use both hands with equal dexterity

to remain neutral in a quarrel (idiom)

to favor or support one side in a conflict or dispute; to be partial or biased