I am quoting Jesus, by the way.
It is a balance.
All who say to Him, “Lord, Lord” shall not enter into the kingdom of heaven. Those also are His words, so you are correct to some degree.
However, he identifies them as those who use His name but are “workers of iniquity.”
So, His people are all those who have “confessed with their mouth the Lord Jesus, and believe(d) in their hearts that God raised Him from the dead.”
It’s an irrefutable bible fact that “whoever believes in Him shall not perish but have everlasting life.”
Indeed, but you are presuming a very modern notion of "believes in Him". Even the devils believe (James 2:19), and they do not have everlasting life.
Did the Arians "believe in Him"?
Jesus said to His Apostles: "The one who listens to you listens to Me, and the one who rejects you rejects Me". (Luke 10:16) That is how we know that the Arians, while claiming to believe in Jesus, actually rejected Him, for they rejected the Church's teachings.
-A8