The term Goy refers to someone who isn't Jewish. There was an article I came across that highlighted that antisemitic Nazis were trying to say that Goyim or Goy is an insult: http://everyday.antisemitism.uk/2016/02/01/graffiti-in-london-says-holocaust-is-a-lie-and-attempts-to-blame-bankers/
I have even come across on Paltalk in the past some taking offense at someone calling me a Gentile or Goyim.
However the term has no offensive connotation and is just simply a term used to describe non Jews. If a Jew called me a Gentile, that's a totally accurate description that causes no offense to me, it is the truth.
Some objection to the term Gentile because by saying "Oh it's a term for pagans, you should not be called that". However this is fallacious, Just because non Jews are called Gentiles, they are not necessarily pagans. In a given context it does refer to pagans but it also refers to Christians who are not Jews but have come from pagan backgrounds and turned from their idols. The term Gentile or nation can still be used by Christians to denote a Christian who has no Jewish background, myself included. We read the following in Acts 15:
"19 Therefore my judgment is that we should not trouble those of the Gentiles (ἐθνῶν or ethnōn) who turn to God, 20 but should write to them to abstain from the things polluted by idols, and from sexual immorality, and from what has been strangled, and from blood. 21 For from ancient generations Moses has had in every city those who proclaim him, for he is read every Sabbath in the synagogues.”
22 Then it seemed good to the apostles and the elders, with the whole church, to choose men from among them and send them to Antioch with Paul and Barnabas. They sent Judas called Barsabbas, and Silas, leading men among the brothers, 23 with the following letter: “The brothers, both the apostles and the elders, to the brothers[c] who are of the Gentiles (ἐθνῶν or ethnōn) in Antioch and Syria and Cilicia, greetings."
Tracey R Rich has a very enlightening article on this topic which I recommend checking out: http://www.jewfaq.org/gentiles.htm
Case and point, the term Goyim or Goy or Gentile are NOT offensive terms and those can be used appropriately by both.
If I am wrong on the usage of the word Gentile, provide your thoughts on the matter.