Can the creation of a labour union actually cause a loss of employment?

In some circumstances, yes. The introduction of a labour union that fights to gain higher wages by using group bargaining tactics could create a minimum wage floor above the pre-existing market equilibrium wage. This would mean that it would be more expensive for firms to hire labour and, especially if above this equilibrium, would mean that the supply of labour would far exceed its demand.

This is because the demand and supply curves are no longer meeting at this new wage level. The difference between the quantity of labour the firm is demanding and the supply of labour people are willing to work at this wage level is called the surplus of labour.

However, if firms are paying workers far below the market equilibrium level then the introduction of a labour union could actually bring the market closer to the equilibrium wage level. Therefore, the effect of a labour union would depend on the existing position of the market equilibrium wage.