Yes, let's look at these verses from AFTER the crucifixtion, closely.
18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.
19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you always, even unto the end of the world. Amen.
from the Greek
3100 matheteuo math-ayt-yoo'-o from 3101; intransitively, to become a pupil; transitively, to disciple, i.e. enrol as scholar:--be disciple, instruct, teach.
1) to be a disciple of one
a) to follow his precepts and instructions
2) to make a disciple
a) to teach, instruct
from the Greek
1484 ethnos eth'-nos probably from 1486; a race (as of the same habit), i.e. a tribe; specially, a foreign (non-Jewish) one (usually, by implication, pagan):--Gentile, heathen, nation, people.
1) a multitude (whether of men or of beasts) associated or living together
a) a company, troop, swarm
2) a multitude of individuals of the same nature or genus
a) the human family
3) a tribe, nation, people group
4) in the OT, foreign nations not worshipping the true God, pagans, Gentiles
5) Paul uses the term for Gentile Christians
Notice that it is pagans and Gentiles that are to be taught. The Jews already know the doctrines,
precepts and commandments which apply to them. The Jews were/are to be a 'light unto the nations'.
from the Greek
1321 didasko did-as'-ko a prolonged (causative) form of a primary verb dao (to learn); to teach (in the same broad application):--teach.
1) to teach
a) to hold discourse with others in order to instruct them, deliver didactic discourses
b) to be a teacher
c) to discharge the office of a teacher, conduct one's self as a teacher
2) to teach one
a) to impart instruction
b) instill doctrine into one
c) the thing taught or enjoined
d) to explain or expound a thing
f) to teach one something
Jesus' disciples and Apostles were to teach all Gentiles in all nations to observe the doctrines and precepts as commanded by Jesus, which was verified to the Jerusalem Council by the Holy Spirit
28 For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things; 29 That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well.
Acts 15 occured about 30 years AFTER the crucifixtion.
from the Greek
5083 tereo tay-reh'-o from teros (a watch; perhaps akin to 2334); to guard (from loss or injury, properly, by keeping the eye upon; and thus differing from 5442, which is properly to prevent escaping; and from 2892, which implies a fortress or full military lines of apparatus), i.e. to note (a prophecy; figuratively, to fulfil a command); by implication, to detain (in custody; figuratively, to maintain); by extension, to withhold (for personal ends; figuratively, to keep unmarried); by extension, to withhold (for personal ends; figuratively, to keep unmarried):--hold fast, keep(- er), (pre-, re-)serve, watch.
1) to attend to carefully, take care of
a) to guard
b) metaph. to keep, one in the state in which he is
c) to observe
d) to reserve: to undergo something
23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.
24 He that loveth me not keepeth not my sayings: and the word which ye hear is not mine, but the Father's which sent me.
Jesus intended the Gentiles of the world learn "Apostolic doctrines" as it existed then and which the early church "steadfastly continued in according to Acts 2:42", or was he referring to Greek Catholic doctrines, Reformation doctrines, or Protestant doctrines which would be created much later? That shouldn't be hard to figure out.
42 And they continued stedfastly in the apostles' doctrine and fellowship, and in breaking of bread, and in prayers.
Remember that Hegesippus records that the Law and Prophets were taught until all the Apostles died off.:
... Up to that period the Church had remained like a virgin pure and uncorrupted: for, if there were any persons who were disposed to tamper with the wholesome rule of the preaching of salvation,11 they still lurked in some dark place of concealment or other. But, when the sacred band of apostles had in various ways closed their lives, and that generation of men to whom it had been vouchsafed to listen to the Godlike Wisdom with their own ears had passed away, then did the confederacy of godless error take its rise through the treachery of false teachers, who, seeing that none of the apostles any longer survived, at length attempted with bare and uplifted head to oppose the preaching of the truth by preaching "knowledge falsely so called."On my arrival at Rome, I drew up a list of the succession of bishops down to Anicetus, whose deacon was Eleutherus. To Anicetus succeeded Soter, and after him came Eleutherus. But in the case of every succession,14 and in every city, the state of affairs is in accordance with the teaching of the Law and of the Prophets and of the Lord....
Therefore was the Church called a virgin, for she was not as yet corrupted by worthless teaching.15 Thebulis it was who, displeased because he was not made bishop, first began to corrupt her by stealth. . . . Each of these leaders in his own private and distinct capacity brought in his own private opinion. From these have come false Christs, false prophets, false apostles-men who have split up the one Church into parts16 through their corrupting doctrines, uttered in disparagement of God and of His Christ....
Taking into account Paul's 'new creature':
2 Corinthians 5
17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.
What did Paul mean by 'new creature'?
2937 ktisis ktis'-is from the root 2936; original formation (properly, the act; by implication, the thing, literally or figuratively):--building, creation, creature, ordinance.
1) the act of founding, establishing, building etc
a) the act of creating, creation
b) creation i.e. thing created
1) of individual things, beings, a creature, a creation
a) anything created
b) after a rabbinical usage (by which a man converted
from idolatry to Judaism was called)
c) the sum or aggregate of things created
c) institution, ordinance
2936 ktizo ktid'-zo probably akin to 2932 (through the idea of proprietorship of the manufacturer); to fabricate, i.e. found (form originally):--create, Creator, make.
1) to make habitable, to people, a place, region, island
a) to found a city, colony, state
2) to create
a) of God creating the worlds
b) to form, shape, i.e. to completely change or transform
Converting from idolatry to Judaism, showing God's proprietorship over us his creations.
When the Apostle Paul instructs Gentiles in Corinth to come to God through Jesus he intends them to become "new creatures" by leaving their idolatry and convert to Judaism and not Catholic or Protestant Christianity as we know it today.
It becomes obvious that Jesus intended for the Gentiles in the various nations of the world to be taught the COMMANDMENTS AND HOW TO CORRECTLY OBSERVE THEM!
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven. Then charged he his disciples that they should tell no man that he was Jesus the Christ." - Matthew 16:13-20
Do we agree that this account is attributed to the apostle Matthew? Do we agree that Matthew is quoting our Lord? Do we agree that if it is written in the Bible, then indeed Christ said this?
You refer to Hegesippus. But, who was Hegesippus? Very little is known of Hegesippus.[ Probably he was a Palestinian Jew, born c. 110, and later converted to Christianity. Under Pope Anicetus (155-166) he undertook a journey throughout Christendom, which led him to Corinth and later to Rome. The purpose of this trip was to collect on the spot the teachings of the various churches which he visited, and to ascertain their uniformity with Rome. He determined in this city the list of the succession of bishops down to Anicetus. On his return to his native land he composed, during the pontificate of Pope Eleutherius (174-189), According to the Paschal Chronicle, he died c. 180.
The work of Hegesippus bears the title of Memoirs ('Upomnhmata). It comprised five books, but is almost entirely lost. We are able, however, to form some idea of the work with the aid of indications and citations furnished by Eusebius. It was not, as St. Jerome would have it, a coherent history of the Church from the passion of our Lord until the middle of the second century, but rather a polemical treatise against the Gnostics, setting forth the facts and the evidence for the truth of the Church's official teaching. Eusebius does not hesitate to rank Hegesippus among the defenders of tradition. "He has narrated," he says, "in a very simple way the infallible tradition of the Apostolic teaching." This is the reason why Hegesippus was so interested in the traditions of the churches and in the succession of the bishops who guaranteed their integrity.
Hegesippus does not seem to have been a very learned man nor a very able writer. His Greek is awkward and he lacked critical acumen; but he was an attentive observer and a sincere witness, highly esteemed by Eusebius.
Eusebius of Caesarea
"At that time [A.D. 150] there flourished in the Church Hegesippus, whom we know from what has gone before, and Dionysius, bishop of Corinth, and another bishop, Pinytus of Crete, and besides these, Philip, and Apollinarius, and Melito, and Musanus, and Modestus, and, finally, Irenaeus. From them has come down to us in writing, the sound and orthodox faith received from tradition" (Church History 4:21).
So, what is your point? Christ handed His church to Peter. Hegesippus, 100 years later, documents the papal descendency.