I’m not a fan of the second idea. The idea might have seemed promising, but that square G just does not want to become the body of a fish.
The first logo is better. However, the thin lines in the fish’s caudal fins, like your professor said, risk filling in at smaller sizes. On the smaller of the two fish, the lines are already beginning to do so. The lines on the pectoral fins, however, are fine since they can’t fill in.
Aside from the lines, the biggest problem I have with the first logo is the lack of compositional relationship between the fish and the words; they come across as two separate things that just happen to be sitting next to each other without a harmonious visual relationship. For that matter, they might even conflict with each other. They both have similar visual weights, which prevents a clear hierarchical relationship. The fish are swimming directly into the words, which is awkward and puts an abrupt halt to the forward motion of the fish. The uppercase is a little bit stiff and formal in relationship to the fish. The thick black line is superfluous and visually intrusive, and it’s not quite centered between the two lines of type. Try to use the same kind of compositional sensitivity you used when positioning the two fish together and extend that kind of thinking to the entire composition, which includes, both the fish and the typography.
Even with all that said, I still like the fish themselves and I think you’re moving in the right direction with it.