For me, there’s a problem with calling God our “Parent” instead of our “Father.” Besides being distracting, it breaks down the felt relationality of the analogy: No one I know calls either of their parents individually their “parent.” Calling God “Parent” makes Him alien.
You might say that God is alien, and that calling things as they are is good. I grant the point. Yet I say that more than that, calling God “Parent,” before foregrounding any actual theological point, foregrounds the supposed sensitivity of the speaker to other people’s theological hang-ups. That’s its purpose.
And even though it does highlight the theological fact of God’s non-sexed alienness and thus can be said to offer a true good, it does so at the cost of losing the greater good: In so-called progressive churches, it’s more important that we linguistically fortify our relationship with God than that we fortify our understanding of His alienness. I’d rather (and occasionally do) call God “Mother” than “Parent.”