extricate
To carefully free yourself from a difficult or trapped situation.
To extricate yourself means to free yourself from a difficult, tangled, or trapped situation through effort, cleverness, or careful work. The word implies you need to actively work your way out, not simply walk away.
Picture a hiker whose backpack straps get caught in thick brambles. She has to carefully work each strap free without tearing the fabric or getting scratched. That's extricating herself. Or imagine realizing halfway through a conversation that you accidentally insulted someone. Now you need to extricate yourself from the awkward situation by apologizing and explaining what you really meant.
You might extricate your hand from a Chinese finger trap, extricate yourself from a commitment you can't keep, or help a friend extricate himself from a friendship that's become unhealthy. The word often appears when someone is stuck (physically or socially) and needs to carefully work their way out.
The opposite of extricate is entangle: getting caught up or trapped in something. When you successfully extricate yourself, you've managed to untangle the mess and get free.