Disconfirmation Bias
We tend to put a higher burden of proof for theories that we don't like / agree with / don't want to believe.
For eg., if we are researching a theory that we agree with, we conclude the search when we encounter one study that agrees with us. But if it is a theory that we don't agree with, we will need 5-6 studies that agree with the theory before it convinces us.
Related: Confirmation Bias