Maybe this idea about the symbolism of fins and scales from the Lubavitcher Rebbe can help:
As the armor that protects the body of the fish, scales represent the quality of integrity, which protects us from the many pitfalls that life presents. A man of integrity will not deceive his customers, in spite of the financial profits involved. He will not lie to a friend, despite the short-term gain from doing so. He will not cheat on his wife, in the face of tremendous temptation. Integrity means that one has absolute standards of right and wrong and is committed to a morality that transcends one’s moods and desires. Integrity preserves our souls from temptation.
Fins, the wing-like organs that propel fish forward, represent ambition. A healthy sense of ambition, knowing one’s strengths and wanting to utilize them in full, gives a person the impetus to traverse the turbulent sea of life and to maximize his or her G‑d-given potential. It propels us to fulfill our dreams and leave our unique imprint on the world.