How can I explain to a non Jewish why bishul akum and Stam wine is prohibited.
You can explain to him that from the time that the Jews went into exile, the Rabbis, including Daniel, (who didn’t eat from the bread of Nebuchadnezzar) sought to preserve the Jewish nation by preventing intermarriage. Therefore they instituted a number of prohibitions to prevent us from socially mixing with the nations, which can eventually to intermarriage. Another reason they forbade some of these things is because if we will eat from their cooking it will eventually lead to the Jew eating something not kosher.
Regarding stam wine, it is partially similar to the above mentioned reason, and also because since the norm in the olden days wine was used as a sacrifice in idol worship, so to remove us from it, the Rabbis prohibited the wine of a gentile, even if he isn’t an idol worshipper.
Avodah Zara 36b, Taz Y:D 123-1, Rambam Hilchos Maachalos Asuros 17-9, Shulchan Aruch Y:D 112-1, 113-1, Aruch Hashulchan Y:D 112-1.