Saul was afraid of David, because Yahweh was with him, and was departed from Saul.
"And made him commander of a thousand"  (1 Samuel 18:13).  If this was a promotion for David, as most of the scholars we have consulted seem to believe, then we may be sure that Saul's motivation included something other than a desire to honor David.  The next verses make it clear what that motivation was.