I am not interested in phrases that contradict what the individual words mean.
I am interested in saying things to newbies that actually make sense.
Clearly an animal’s soul is not material (hence it must be immaterial and therefore unseen and therefore “spiritual”) and equally clearly it does not last beyond death.
The word “spiritual” has a number of different meanings which you may not accept but most english speakers do. The CCC does not contradict what I stated, nor will you see in it a reference to animals having “material souls”. That is in fact a paraphrase of Aristotle, and not a particularly good one at that.
When the Church speaks of a “spiritual soul” the phrase is usually meant as a loose expression for “rational soul” or “immortal soul” mde in Gods image… ie distinuishing human life from animal life.