In the economy of the Trinity, God has eternally existed in a communion of love. This is hard for us to understand, because love necessitates a subject-object interplay. If God is One and self-sustaining, what is there to love beside Himself in the absence of created beings, like ourselves? Church Fathers used a word, perichoreo, to describe not only the relationship between Christ’s two natures but also the “interpenetration” of the three Persons of the Trinity. The Will/Word of God eternally coexists with His very nature (John 1:1). The thing that is uttered is the Son, ο λόγος, while the love that binds them is a Person in and of itself because the Love of God is indistinguishable from His essence, same as His Word is. The key here is that this is not temporal procession, but eternal procession. God has always existed in this way. His Word takes on different forms in different times, and finds its consummation in Christ, the Word made flesh.
But you asked about the Holy Spirit proceeding from the Father and the Son. I don’t know if your friend is concerned about the filioque clause, or if the term “procession” is just confusing. The original Greek term is εκπορεύομαι. It has the denotation of going, or being poured forth from, or proceeding. It’s a term that helps us to see how the Holy Spirit is the natural outcome of that Father/Son relationship. Orthodox Christians don’t like saying “proceeds from the Father and the Son,” because the Father is the ultimate source of everything. But Catholics are okay with adding “and the Son” because everything the Father has He gives to the Son.
I’m not a theologian, but this is how I’ve understood it in my mind for a long time and I hope I help even in the slightest.
my response doesn’t make this mistake, though, or at least how I understand it.