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 so naming God foregrounds the fact that God is alien, that He is neither male nor female. But I say that more than that, it foregrounds the supposed sensitivity of the speaker to other people’s theological hang-ups, and even though it does highlight the theological fact of God’s non-sexedness and thus can be said to offer a true good, it does so at the cost of losing the greater good: In the so-called progressive churches, it is 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 call Him “Parent.”