I was looking at a map of countries whose languages are of the Indo-European family, and I couldn’t help but notice that Hungary is not one of them. This is especially glaring because all of the countries surrounding Hungary have languages from that family. Why is this?
this person has done a (IMO) great job of explaining it.
Tldr, Indo europeans usually refer to a civilization that migrated from ukraine/southern russia to europe while the magyar (hungarians) come from the ural and siberia where the people spoke ugrian languages instead of indo european ones. When the magyar tribes invaded the carpathian bassin they retained their own language although it changed (as all languages do) a little bit over time. That is why the magyar language is in the uralic languages group and not the indo european one