Why do you say it's wrong to identify as a Gentile?

There are those who, based on certain spiritual positions, maintain a type of behavior related according to the interpretation they give to some verses of the bible. In this case we will talk about the meaning, about who the Gentiles are.

Goi is a Hebrew word, which is sometimes interpreted in a derogatory way and literally means Nation and its plural is Goim. Therefore Goi refers to non-Jewish people and nations. This is how it appears in the Bible (Bereshit / Genesis 10: 5)

Gentile refers to the goi, a term used by Jews to refer to nations or non-Jewish individuals.

Pagans, a term that is usually applied to people who have religious beliefs different from Christianity.

The biblical meaning of Gentiles refers to the non-Jewish, pagan or foreign person. Sometimes this word refers to Israel. It appears in the New Testament and in the times of peace it was agreed a kind treatment to the Gentiles under the Old Testament law.

For many people the gentle expression refers to it as an identification that is related to the spiritual area, and that by mistake they call themselves Gentiles, literally ignoring the true biblical meaning. Therefore, when someone says I AM GENTILE, what they are saying is that they do not believe in God.
Citan:

In 1 Corinthians 12: 2: "You know that when you WERE GENTILE, you went astray, taking you, as you were led, to the mute idols"

Matthew 18:17, thus: "If I do not hear them, tell it to the church; and if he does not hear the church, have him for GENTIL and publican "

Matthew 6: 7, says: "And praying, do not use vain repetitions, like THE GENTILES, who think that by their verbiage they will be heard."

Other people claim that when God spoke with Abram and told him to go the land that will one day be called the land of Israel, he promised that one day he will become a great nation. This means that God's promise to Abram is also related to other nations. God said that the other families of Earth will be blessed through Abram. Therefore, anyone who remains in the faith of the true God will be recognized as a child of God, regardless of their origin or nation.

The writer Pater Fausto Osuna makes a clarification on the aforementioned terms

Etymological difference: Gentile, comes from the Hebrew "goy" (plural, "goyim"), from the Greek "ethne", from the Latin "gene, gentis", which means: people, nations. Whereas the pagan term comes (only) from the Latin "paganus", which means "inhabitant of the countryside", "rustic", of the village.

Chronological difference: the Gentile word is much older, since it is the one that uses the Bible, from the Hebrew, the Greek and finally the Latin. While the word pagan comes from Latin, which is not originally a biblical language, but even translations, especially the translation of St. Jerome known as the Vulgate Bible.
At first, God did not allow religious and cultural mixture in the Jewish people, but with the arrival of Christ and the Gospel, what Paul says is "now there is no difference between Jew and Gentile, slave and free" (Gal 3,28). -29), we are all one in Christ. This process of moving from an exclusive people to an Inclusive People is the design of God who calls us to live the unity of the Church, overcoming all discrimination and exclusion.

Even, being clear in the concepts, I think, what is important is what we learned from Jesus, by showing us that the times of God are perfect, his teachings ended up uniting the Jews and the Gentiles.