That's not how it works in countries with stronger protections. Unions don't have the power to fire anyone, nor do they have veto power. There are rules (e.g. no firing without a cause from a whitelist of acceptable causes that typically come with additional requirements), and courts to decide cases where there are disagreements over the rules.
Sure, but for this part of the equation, the employer wants someone to go. The union (or the labor representative in the company, it's not necessarily a union) decides whether that's okay, or whether they want to fight it. You still want to work with your labor representation as an employer and if you're not hellbent on getting rid of someone, you'll accept what they decide.
That gives them power, for example over non-union employees of the company.