John Gill Commentary 2 Samuel 2:19

"And Asahel pursued after Abner; and in going he turned not to the right hand nor to the left from following Abner." — 2 Samuel 2:19 (ASV)

And Asahel pursued after Abner
Ambitious of the glory of taking or slaying the general of the army of Israel; trusting to his swiftness, not considering that the race is not always to the swift, and that he had to do with a veteran soldier, and he a raw young man, though valiant:

and in going he turned not to the right hand nor to the left in
following Abner ;
he kept his eye upon him, and pursued him closely, disregarding persons on the right or left he could have made prisoners; but those he neglected, being bent on taking Abner if possible.