OK, lets look at Psa 51:5;
Psa 51:5 Behold, I was shapen in iniquity; and in sin did my mother conceive me.
Does this verse say David inherited a sin nature from his father? NO, it does not even mention his father. If anything, if this verse was teaching that you inherit a sin nature, it would teach that David inherited his sin nature from his mother!
David did not have the same mother as his seven brothers. They were all tall and handsome, David was short and ruddy.
David's mother had relations with a non-Jew. David had two sisters Abigail and Zeruiah whose father was Nahash the Ammonite.
2 Sam 17:25 And Absalom made Amasa captain of the host instead of Joab: which Amasa was a man's son, whose name was Ithra an Israelite, that went in to
Abigail the daughter of Nahash, sister to Zeruiah Joab's mother.
1 Sam 2:13 And Jesse begat his firstborn Eliab, and Abinadab the second, and Shimma the third,
14 Nethaneel the fourth, Raddai the fifth,
15 Ozem the sixth,
David the seventh:
16 Whose sisters were Zeruiah, and Abigail. And the sons of Zeruiah; Abishai, and Joab, and Asahel, three.
David's mother, whose name is never mentioned in scripture had two daughters with Nahash the Ammonite. This was considered "unclean" to the Jews, she would have been a "polluted" woman.
David was the black sheep of his family. When Samuel came to Jesse and asked to see all his sons, twice Samuel did not bring David. Only the third time, when Samuel insisted, did he bring David forward, and Samuel annointed him as the next king of Israel.
1 Sam 16:10 Again, Jesse made
seven of his sons to pass before Samuel. And Samuel said unto Jesse, The LORD hath not chosen these.
11 And Samuel said unto Jesse, Are here all thy children? And he said,
There remaineth yet the youngest, and, behold, he keepeth the sheep. And Samuel said unto Jesse, Send and fetch him: for we will not sit down till he come hither.
12 And he sent, and brought him in. Now he was ruddy, and withal of a beautiful countenance, and goodly to look to. And the LORD said, Arise, anoint him: for this is he.
But nevertheless, it seems David had a poor self image because of his mother, and many scholars believe this is what David was saying in Psa 51:5.
It is also possible that David was conceived out of wedlock, but scholars are not completely sure.
But this verse in no way is teaching that all men are born sinners or that they inherit a sin nature from their father.