Unionization is forming a monopoly on the supply of labor. Just as with monopolies in other industries, it can lead to anti-competitive behavior.
There are situations in the real world where the government grants companies exclusivity. Just as in the real world, there is a rationale behind unionization.
In both instances it can be exploited and lead to poor product at a high cost.
I think the better approach would be to have competing unions. Allow unionization, but also require multiple unions in one field. This would give indvidual workers increased bargaining power vs the employer (the initial reason for the union), but would not allow the union to have a monopoly on the supply of labor.
but hey... this isn't really a discussion on unions, more an amusement at the convoluted logic the religious university was using.