Allowing employees to have a secret ballot when they vote on unionization is appropriate for two reasons. First, it protects the workers themselves. Second, it protects the employers and the unions.
In our modern political system, we always allow people to vote in secret. We do this because we know that this protects the voters from being pressured. The same is true of workers when voting on unionization. If workers do not have the secret ballot, they can be pressured either by their fellow workers or by their employers. Employers might threaten to fire them if they vote for unionization. Coworkers might make their lives miserable if they do not vote for unionization. Either way, a secret ballot protects the workers from retaliation based on how they voted.
Secondly, a secret ballot is ultimately in the best interests of the union and the employer. If there is no secret ballot, workers can be pressured one way or the other. In that case, the unions and the employers might lose out not on the merits of their case but because the other side was better at intimidating the workers. With a secret ballot, the two sides know that they have a better chance to win “fair and square.”