When the Good Shepherd chose His 12 sheep all 12 of them were good sheep. To say otherwise makes Jesus not such a Good Shepherd, right? What shepherd in their right mind will allow a dangerous sheep (wolf) amongst their flock? (See John 10:1-16)
Judas was chosen by the Good Shepherd but he later chose to betray the Shepherd.
Jesus answered them, Have not I chosen you twelve, and one of you is a devil? He spake of Judas Iscariot the son of Simon: for he it was that should betray him, being one of the twelve. John 6:70-71
BETRA'Y, verb transitive [Latin traho.]
To deliver into the hands of an enemy by treachery or fraud, in violation of trust.
To violate by fraud, or unfaithfulness; as, to betray a trust.
To violate confidence by disclosing a secret, or that which was intrusted; to expose; followed by the person, or the thing; as, my friend betrayed me, or betrayed the secret.
To disclose, or permit to appear, what is intended to be kept secret, or what prudence would conceal.
To mislead or expose to inconvenience not foreseen; as, great confidence betrays a man into errors.
To fail, or deceive.
And when it was day, he called unto him his disciples: and of them he chose twelve, whom also he named apostles; Simon, (whom he also named Peter,) and Andrew his brother, James and John, Philip and Bartholomew, Matthew and Thomas, James the son of Alphaeus, and Simon called Zelotes, And Judas the brother of James, and Judas Iscariot, which also was the traitor. Luke 6:13-16
TRA'ITOR, noun [Latin traditor; trado, to deliver.]
One who violates his allegiance and betrays his country; one guilty of treason; one who, in breach of trust, delivers his country to its enemy, or any fort or place entrusted to his defense, or who surrenders an army or body of troops to the enemy, unless when vanquished; or one who takes arms and levies war against his country; or one who aids an enemy in conquering his country. [See Treason.]
One who betrays his trust.
At the onset Judas was indeed trusted and chosen by Jesus but Judas later betrayed this trust and thus was counted a traitor towards God.
He was once saved but forfeited his position by betraying the Saviour of his own soul.
You can do the same if you do not take heed as Paul and the writer of Hebrews so clearly warned.
Wherefore let him that thinketh he standeth take heed lest he fall. 1 Corinthians 10:12
Take heed, brethren, lest there be in any of you an evil heart of unbelief, in departing from the living God. Hebrews 3:12