"The things which you have heard from me in the presence of many witnesses, entrust these to faithful men who will be able to teach others also." 2 Timothy 2:2. It sure looks like apostolic succession to me.
No, that scripture does not support the Catholic’s Apostolic Succession. There is no absolute surety in the Bible that no one will not fall into falseness and thus teach error. Even Paul had to rebuke Peter. The Catholics claim their popes have succeeded from Peter, but there is not such teaching in the Bible. That is a manufactured belief by the Catholics. In fact, that teaching of the Catholics shows favoritism and the Bible forbids favoritism.
1 Corinthians 1:11-12 My brothers, some from Chloe's household have informed me that there are quarrels among you. 12What I mean is this: One of you says, "I follow Paul"; another, "I follow Apollos"; another, "I follow Cephas"; still another, "I follow Christ." 13 Is Christ divided? Was Paul crucified for you? Were you baptized in the name of Paul?
1 Corinthians 3:1Brothers, I could not address you as spiritual but as worldly—mere infants in Christ. 2I gave you milk, not solid food, for you were not yet ready for it. Indeed, you are still not ready. 3You are still worldly. For since there is jealousy and quarreling among you, are you not worldly? Are you not acting like mere men? 4For when one says, "I follow Paul," and another, "I follow Apollos," are you not mere men?
5What, after all, is Apollos? And what is Paul? Only servants, through whom you came to believe—as the Lord has assigned to each his task. 6I planted the seed, Apollos watered it, but God made it grow. 7So neither he who plants nor he who waters is anything, but only God, who makes things grow. 8The man who plants and the man who waters have one purpose, and each will be rewarded according to his own labor. 9For we are God's fellow workers; you are God's field, God's building.
1 Corinthians 3:18 Do not deceive yourselves. If any one of you thinks he is wise by the standards of this age, he should become a "fool" so that he may become wise. 19For the wisdom of this world is foolishness in God's sight. As it is written: "He catches the wise in their craftiness“; 20and again, "The Lord knows that the thoughts of the wise are futile.” 21So then, no more boasting about men! All things are yours, 22whether Paul or Apollos or Cephas or the world or life or death or the present or the future—all are yours, 23and you are of Christ, and Christ is of God.
1 Corinthians 4:6 Now brothers, I have applied these things to myself and Apollos for your benefit, so that you may learn from us the meaning of the saying, "Do not go beyond what is written.” Then you will not take pride in one man over against another.
Paul even warns that when he leaves savage wolves will come in among them.
Acts 20:29 Iknow that after I leave, savage wolves will come in among you and will not spare the flock.