Do Numbers 6:5 and 1 Corinthians 11:14 contradict? What does Apostle Paul mean in 1 Corinthians 11:14?

Some preachers of other sects say if only Samson lived in the time of Jesus, he will be scolded by Jesus because of Apostle Paul said. 

"Does not nature itself teach you that if a man wears long hair, it is degrading to him"(1 Corinthians 11:14)

The problem with those who read the Bible is they read the Bible in English and Tagalog and they insist on their own interpretation without deep analysis according to that of scholars who studied the original text, culture, and historical background of Bible verses. 

Let us remember that the Apostle Paul wrote 1 Corinthians 11:14. If Apostle Paul says long hair is unnatural for men, why do our portraits of Jesus show him with it?

What is Nazirite? 

According to the Historical Dictionary of Jesus by Daniel J. Harrington on page 111:

According to Num 6:1–21, men or women might consecrate
themselves to God as nazirites for a specific period with a special
vow. During this time, they were to abstain from wine, let their
hair grow, and avoid contact with corpses. The accounts of the births
of Samson (Judg 13:4–14) and Samuel (1 Sam 1:11) suggest that an
infant might be consecrated as a nazirite to God. In Luke 1:15, John
the Baptist is described in nazirite terms (“he must never drink wine
or strong drink”). The designation of Jesus as a “Nazorean” in Matt
2:23 may also be associated with his status as a nazirite. According to
Acts 18:18 and 21:20–26, Paul participated in the rituals connected
with closing a period of observing a nazirite vow. 

Here is the analysis of credible Bible scholars. They carefully understand the context and historical background of said verses:

Thus Paul IS NOT ARGUING THAT MEN MUST WEAR THEIR HAIR SHORT, or that women must have long hair, as though "nature" meant some kind of "created order."1 6 Indeed, the very appeal to "nature" in this way suggests most strongly that the argument is by way of analogy, not of necessity. As in the two preceding arguments (vv. 4-6, 7-12), Paul begins with the man in order to set up what he wants to say about the woman. What "nature" thus teaches is that "man, on the one hand,  if he has long hair, it is a disgrace  to him." This seems to be clear evidence that by "nature" Paul meant the natural feelings of their contemporary culture. AFTER ALL, ACCORDING TO ACTS 18:18 PAUL HAD APPARENTLY WORN LONG HAIR FOR A TIME IN CORINTH AS PART OF A VOW. (New International Commentary on the New Testament (THE FIRST EPISTLE TO THE CORINTHIANS), p. 527)

Aside from that, one exegetical commentary on Acts (Zondervan Exegetical Commentary on the New Testament) was analyzed by a credible scholar named Eckhard J. Schnabel:

“Before Paul embarked on the ship to Syria, HE HAD HIS HAIR CUT BECAUSE HE HAD MADE A VOW…What did Paul hope to achieve with a Nazirite vow? One suggestion has been that Paul wanted to demonstrate his “willingness to follow the Torah in matters of personal spiritual discipline” and thus his “good faith” to the conservative Jewish Christians in Antioch and in Jerusalem, hoping that this gesture “would heal any continuing rift”(Exegetical Commentary on the New Testament,  Acts, Eckhard J. Schnabel, p.767)

What does 1 Corinthians 11:14 mean? 

Let us look at the historical background since he said this to the Corinthians. 

 Long before Paul's day Corinth had the reputation for being sexually promiscuous. In fact the word 'Corinth' was a moniker for fornication. In his first letter to the Corinthian church, Paul claims: 'It is actually reported that there is sexual immorality among you' (1 Corinthians 5:1). The Roman Historian and geographer Strabo, who wrote the early decades AD, reports that there was a temple of Aphrodite on the Acrocorinth, the Acropolis at the edge of the city which is perfected on a mountain that stands 1,886 feet (575 m) above sea level. He also records that it had 'a thousand temple slaves, prostitutes, whom both men and women had dedicated to the goddess'. (The Archaeology of the Bible,  James K. Hoffmeier, p. 178)

It was also mentioned that Aphrodite has a temple.

According to history, both men and woman had dedicated to the goddess.

The old view that made Corinth almost synonymous with prostitution should be abandoned. Aristophanes (Fragments 354) did use “to Corinthianize” (κορινθιάζεσθαι) as a verb for dissipated living, and plays entitled The Corinthian (Philetaerus 13.559a; Poliochus 7.31.3c) made that name interchangeable with whoremonger. But these writers refer to Greek Corinth, destroyed in 146 B.C., not to Corinth after it had been resettled and rebuilt as a Roman colony. It is anachronistic to apply these epithets to the Corinth of Paul’s day. Often cited is Strabo’s (Geogr. 8.6.20) reference to one thousand temple prostitutes dedicated to Aphrodite: “And the temple of Aphrodite was so rich that it owned more than a thousand temple-slaves, prostitutes, whom both men and women had dedicated to the goddess. And therefore it was also on account of these women that the city was crowded and grew rich” (1 Corinthians (Baker Exegetical Commentary on the New Testament), David E. Garland, p. 240).

Some may ask why we get proof from others? We base our analysis on the assessment made by credible scholars who better understand exegesis and historical background of said verses. We cannot entrust this to people who merely read the Bible translations who tried to understand the text based on their own interpretation.

According to history, there are long-haired male prostitutes in Corinth.

High on the Acropolis, overlooking Corinth and dominating its life, was the magnificent temple of Aphrodite, the goddess of love and fertility. One thousand priestesses plied the trade of prostitution as part of the religious rites. Corinth was a vice-oriented city. Long-haired male prostitutes were a common sight on the streets and were the background for Paul's comment in 1 Cor. 11:14, "Doth not even nature itself teach you, that if a man have long hair it is a shame unto him?"(The Corinthian Catastrophe, p. 15, George E. Gardiner)