Remove the obstruction

Attempting to remove the object someone is choking on with your fingers can be dangerous for several reasons:

1. Risk of Pushing the Object Deeper: Manually trying to remove the object can inadvertently push it further down the airway, making the obstruction more severe and more difficult to dislodge.

2. Potential for Injury: Inserting fingers into the victim's mouth can cause trauma to the soft tissues of the throat and mouth, potentially leading to swelling, bleeding, and further complications.

3. Loss of Time: Attempting to manually remove the object can waste precious time that should be used to perform back blows and abdominal thrusts, which are more effective at expelling the object from the airway.

4. Increased Risk of Aspiration: A partially dislodged object might be moved in such a way that it is inhaled deeper into the respiratory tract, increasing the risk of complete airway blockage or aspiration into the lungs.

5. Reflexive Biting: The person choking may reflexively bite down due to panic or hypoxia, potentially injuring the rescuer's fingers and complicating the rescue effort.

For these reasons, it is safer and more effective to use established techniques such as back blows and abdominal thrusts to clear the airway. 

If the object is visible and easily reachable without the risk of pushing it deeper, careful removal may be considered, but only if done with extreme caution.