Leverage comes from alternatives to an agreement.
The asymmetry in negotiations is that in most circumstances, employees or candidates tend to have zero (remaining unemployed) or one (remaining at a job) alternatives.
People think they have more alternatives, but there's a huge difference between an alternative at an exact moment, and alternatives that are theoretical within days, weeks or months.
Employers have alternatives, even if they aren't great, right now. So you're not on an equal footing whether you are interviewing or talking to your current employer.
Not to mention, when you do have leverage, exploiting it to the hilt can poison or destroy a future relationship.