And neither can a Spirit of Man unless you, yourself have the healing spell. (which is not a guarantee).
For the spirit of Man to be able to cast, you also have to summon him at a correct level of Force for this to even be an issue. (Force 3+)
So that is a lot of IFs for "Spirit of Man" as "Healing" spirits (which isn't even a category of spirit in SR, it's "Health", as in ALL the health spells)
But, they and any other health spirit can do, is Aid sorcery to augment you casting of a health spell (ANY health spell).
Which, BTW the is all any spirit of any class can do..
Fire spirits don't cast fireballs (no sorcery skill remember); But they do have elemental attack (which is NOT to be confused with fireball!)
And this seems to be a large problem with many people. They automatically look and see that no Spirit can cast spells and go "WTF, this has to be wrong" When it's not. Many people ascribe abilities to spirits that they just don't have, sometimes they do this flippantly (like when some people say: "And the fire spirit just fire balls them")
Spirits, while very powerful, are also very limited.
An Unbound Spirit can only do the following things:
Combat
POWER use
PHYSICAL task
Remote Service
A Bound spirit can all of that, plus the following:
AID alchemcy, sorcery, or study in it's sphere of influence. So a shaman could summon a spirit of Water, and get is aids in casting any Dectection spells the shaman may have and want to cast. BUT the spirit itself can not cast a single spell.
Sustain a Spell YOU have cast and initially taken drain for, and only for (FORCE) turns
Bind a spell for (FORCE) days, but the spirit loses 1 rank of Force per day...
And lastly; You're Meta-Gaming. All you are doing to looking at a stat block of numbers and saying "WTF this is Wrong" with out looking at the traditions and the spirits on the whole of what they are. Which is a metrophical outlook of life.
Take a look at Shamanic Tradition and their spirits. They all make sense in the Shamanic sense of the "power elements" and the categories of Magic.
Violence and Combat under Beast Spirits (like Bear, or Wolverine, Or Shark, Or....)
Health, welfare and nuturment in Earth (the Mountain, the Forest, the Spring, the Brooke)
Manipulation in Spirits of Man (Lying, Cheating, Greed, Lust, Rage, Contempt)
Dectection in Water Spirits (Purity, Truth, Washing away the lies)
Illusion in Air Spirits (whispers, half truths, Fog)
but have said before. do as you will.