Jews don't believe that the G-d of Abraham and Sarah is perfect in love, not yet anyway. Some of our theology suggests that the reason we exist is so G-d could learn how to love better. Humanity evolves, and if humanity was created in G-d's image, why doesn't G-d evolve as well?
It is Christianity that defines G-d as "all-loving," "unchangeable," "perfect." It isn't that Jews don't also see this as part of the entire G-d concept they hold in their theology. It is just far more advanced and dimensional than that.
One of the texts that Jews use as the basis for this theology is Numbers 15 where a man is put do death by stoning for picking up wood on the Sabbath. G-d not only demands stoning but the Jewish people themselves carry out the judgment.
Think about it. There was no previous law stated that the man could have avoided if he knew about it. The law is promulgated after the man gathers the wood, as well as the penalty. It was a cruel and unforgiving judgment, and Judaism recognizes this, so much so that we never forgot it and made it a part of our Law.
Today things are different in regard to G-d and Jews. Today such an action by the Jewish people would be unjust (though this doesn't mean there aren't some among us Jews who believe we should be as unbending with those we view as enemies). The Jewish concept of G-d is that we have evolved because G-d has evolved, and that neither of us engages in stoning people or demanding such stoning. We've grown up, but we also acknowledge we've both grown up together--and sometimes out of very dark pasts.
Jews reject the simplistic idea of a "perfect" G-d. They view such concepts as infantile, dysfunctional and immature, much like the idealistic image one has of their parents that gets crushed by reality as they become adults themselves. Who makes up these false images of their parents? We do. Our parents are not to blame for failing to live up to our childish expectations, and neither is G-d (though Christians would have you think differently).
Like Moses, we feel we each have something to offer in making G-d more complete, even changing his mind from doing something. (Exodus 32.14) In the Jewish view we DO NOT "LISTEN AND OBEY." We argue, debate, challenge, and wrestle with G-d. (Genesis 18.22-33; Jonah 4; Genesis 32.23-31) We are indeed in a covenant together, us and G-d, but we are in it together.
We as humans have a drive to challenge ourselves at times, to become more than what we are now, to refuse to be satisfied in our current state. True, not everyone has these drives, but many do. If humans have them, then why not G-d if we are made in the image of our Creator?