Can a Woman Be Spiritual Director of a Man

No.

The reason is very simple. Lust.

A typical male weakness is his inordinate sexual drive; he cannot hide it in spiritual direction, on the one hand; and it would be too great a scandal for the woman director to handle, on the other hand. He would be damned if he did and damned if he didn't reveal it. Perplexed!

A man, however, with proper caution (e.g. a confessional wall and screen always between them), can very effectively direct women in spiritual direction because the woman is more prone to sexual innocence than the man. His judgement of her will always be favorable and objective because she is normally remarkably much better than he in this area of greatest shame for him! He is able to help her in her specific weaknesses because he is all the more aware of his own faults.