What are the Biblical arguments against man having an immortal soul separate from the body? Belief in an immortal soul seems quite common in Christianity although some denominations do not seem to believe in this.

What specific scriptures, and scriptural arguments, are used by those that do not believe in humans having an immortal soul separate from the body?

Update: this is not a duplicate of this other question because this one is specifically asking for support for the opposite viewpoint. Additionally the other question has only answers which support the idea that humans do have a soul. If this has to be scoped to a particular denomination, I choose Jehovah's Witnesses.
I am answering from the perspective of Jehovah's Witnesses.
In the Bible, the word for soul is ne'phesh in Hebrew, and psy'khe in Greek. Their definitions generally convey the concept of &quot;a breathing creature&quot; or &quot;a living being&quot;. Many of the scriptures I mention in this answer may not use the word &quot;soul&quot; in their English translations, but will use one of these similar terms such as &quot;life&quot;, &quot;person&quot;, &quot;creature&quot;, or &quot;body&quot;. I've denoted these words with the word &quot;soul&quot; in brackets next to them.
Adam wasn't given a soul, he became a soul.

And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. - Genesis 2:7 (KJV)
So also it is written, The first man Adam became a living soul. The last Adam became a life-giving spirit. - 1 Corinthians 15:45 (ASV)

The soul can die.

... the soul that sinneth, it shall die. - Ezekiel 18:4 (KJV)
He must not enter a place where there is a dead body [&quot;soul&quot;]. He must not make himself unclean, even for his father or mother - Leviticus 21:11 (NIV)
All the days that he separateth himself unto Jehovah he shall not come near to a dead body [&quot;soul&quot;]. - Numbers 6:6 (ASV)
And they smote all the souls that were therein with the edge of the sword, utterly destroying them: there was not any left to breathe: and he burnt Hazor with fire. - Joshua 11:11 (KJV)
Samson said, “Let me [&quot;my soul&quot;] die with the Philistines!” Then he pushed with all his might, and down came the temple on the rulers and all the people in it. Thus he killed many more when he died than while he lived. - Judges 16:30 (NIV)
Do not be afraid of those who kill the body but cannot kill the soul. Rather, be afraid of the One who can destroy both soul and body in hell. - Matthew 10:28 (NIV)

Animals are souls, and die the same way.

Then God said, “Let the waters teem with swarms of living creatures [&quot;souls&quot;], and let birds fly above the earth in the open expanse of the heavens.” - Genesis 1:20 (NASB)
Then God said, “Let the earth bring forth living creatures [&quot;souls&quot;] after their kind: cattle and creeping things and beasts of the earth after their kind”; and it was so. - Genesis 1:24 (NASB)
For the fate of the sons of men and the fate of beasts is the same. As one dies so dies the other; indeed, they all have the same breath and there is no advantage for man over beast, for all is vanity. - Ecclesiastes 3:19 (NASB)
8 The second angel sounded his trumpet, and something like a huge mountain, all ablaze, was thrown into the sea. A third of the sea turned into blood, 9 a third of the living creatures [&quot;souls&quot;] in the sea died, and a third of the ships were destroyed. - Revelation 8:8-9 (NIV)

There is also a non-biblical argument against the immortality of the soul, and that is that the teachings originated from Socrates and Plato, and was later incorporated by Christian Greek philosophers.
For more information, there is What Is the Soul? and Insight, Vol. 2.