Gen.2:7 says that "God proceeded to..blow into his (Adams) nostrils…and the man became a living soul." Elsewhere in the Hebrew text animals are spoken of as "souls" (Gen.1:20; Num,31:28 ect)It seems to me a soul is what we are, not something we have. Eccl.3:19 says that at death man has no superiority over the animals. While Eze.18:4 says that the soul that sins itself will die, therefore the soul is not immortal. This would seem to support this idea. What do you think?
I believe this is a language/vocabulary issue rather than a theological one. I am NOT an expert in Hebrew. I am not even an amateur in Hebrew. However, I am prepared to give my uneducated guess. Even in English we use the word "soul" with different connotations. We use the word soul to mean a person. Twenty souls perished in the tragedy. We also use it in the more more common biblical sense as something we have. Twenty persons who had souls perished in the tragedy. These two sentences are not logical contradictions. They use the word soul in more than one way.
As for Genesis 1:20 and Numbers 31:28, most translations do not have soul here. I am guessing that you are using the King James. Possibly (I have not done the research!) this is the only translation which has soul in these two passages. As you know, the KJV uses words with an archaic definition, so you should be cautious about how you use this translation. The majority of scholars, apparently, did not feel the Hebrew being used here is equivalent to the word soul in English. I definitely would NOT use Genesis 1:20 or Numbers 31:28 to teach that animals either have or are souls.
The Jews were not as careful about language as we, with a Western mindset, might prefer them to have been. Based in the different ways the word soul is used in the Old Testament, I believe that you could make an argument that both statements are true. We have a soul and we are a soul. In Ezekiel 18:4 the language being used is such that the implication is that we ARE a soul. In Genesis 2:7 language is being used in which the implication might be (or it might not be!) that we have a soul. We might be able to translate/interpret Genesis 2:7 to say that God made Adam alive, or we might interpret it to say that God put a soul and spirit into Adam. Both interpretation are possible, in my opinion.
Philosophers and careful theologians will, of course, use vocabulary more carefully that the OT writers. You, too, should be careful in how you use the word. So….. If you define the English word soul in a way so that we ARE a soul, then you can stick with this definition and defend the theology that people are souls. Conversely, if you define the English word soul in a way so that we HAVE a soul, then you can stick with this definition and defend the theology that people have a soul.
In the translation I am using (NIV), Eccl 3:19 has "spirit" rather than "soul." Again, because of vocabulary issues, I believe we should be cautious about creating sharp distinctions between a human soul and a human spirit based on a singly passage in Hebrew. Of course, you know that Hebrews 3:12 tells us that scripture can divide between soul and spirit!!! However, this passage implies that the distinction is a hard one to draw. In Ezekiel 18:4, the translations are more in agreement with using the word "soul." However, in this context, the word is used in a more generic sense. As I see it, it is in the sense of my quote above: twenty souls perished in the tragedy. The meaning of Ezekiel 18:4 is such that we could translate it as The one who sins is the one who will die. It is NOT implying that our souls are not immortal. It is implying that if we sin we will suffer spiritual death–that we will go to hell. I am confident that Ezekiel is talking about spiritual life and death because if he were not, then the converse of the statement "the soul who sins shall die" would be that the soul (ie the person) who does not sin will be immortal. We know that human beings are definitely not immortal. I hope this will get you started. You might want to seek the input of an expert in the Hebrew language for deeper insight.