Clearly God has shown us that He is a loving Father and He spoke in that term. Jesus was His Son, the Second Person of the Trinity, who came down to earth to be like man was. This was done so that we can understand God’s love.
Without using this analogy, which God wants us to, we may not give an appropriate picture of what and who God is as He wants us to know Him.
Hypothetically without using that analogy, my next best example would be that God is the Good Shepherd.
Here we need to explain the relation of the sheep with the traditional understanding of the shepherd. The sheep being naive and vulnerable on their own are therefore easy prey to the enemies - the wolves. The environment for them can be hostile - there are deserts and ravines where they can get lost or fall into and get injured.
However, the shepherd knows about his sheep, sometimes even the individual sheep. He guards his sheep and know exactly what their danger are. He will look for them, call them by names and if necessary spends hours and days looking for the lost ones. He does all the necessities to keep them safe, and he may sacrifice his time and life to do that.
If the sheep are injured or sick, he will attend to them. He also always bring them to a safe place where food is aplenty (green pasture).
The explanation of the shepherd and the sheep to depicts God relations with us is very touching and convincing to me, besides being biblical too. (Ezekiel 34, Psalm 23, Gospel John 10)