A.T. Robertson Commentary Mark 6:26

"And the king was exceeding sorry; but for the sake of his oaths, and of them that sat at meat, he would not reject her." — Mark 6:26 (ASV)

He would not reject her (ουκ ηθελησεν αθετησα αυτην). He was caught once again between his conscience and his environment. Like many since his day the environment stifled his conscience.