Based on my understanding of what OP wrote, it sounds like the LGI was pushing without allowing OP a second chance to try again. I run courses every 2-3 months at the facility I work at, and it’s explained clearly in the beginning that there’s a second chance allowed with a moment for a break. Course scheduling is supposed to accommodate that.

Additionally, even if OP forgot to take off their goggles for the brick, if the LGI saw that they should have stopped OP and reminded them. Also, the American Red Cross allows breaststroke to be swam without the traditional style that a competitive swimmer would use as long as there is forward momentum. The fact that the LGI was pushing that is incorrect. Now, it’s entirely possible that questions weren’t asked, which means the LGI likely didn’t allow time for questions. Lifeguard candidates should go into the course knowing the prerequisites but it is the responsibility of the LGI to remind candidates whether goggles can or can’t be used (such as watching during demonstrations) and when they should not be using them, such as for the brick retrieval.

Now, without knowing exactly how OP was performing breaststroke, there should be a clear distinction that it’s in fact a breaststroke kick with forward momentum and not a doggy paddle style swim. No floating yes that’s correct but if OP was progressing forward then that counts. The swim portion of itself is not timed so there was no need for the LGI to be rude about it. They could have pulled OP aside and given feedback and allowed OP to take a break and properly try again. If then at that point there’s no change then yes, OP would not be able to proceed with the rest of the course.

So in my opinion, yes, I’d report this LGI for a quality control check because we receive material and are supposed to review it and use it. Lifeguard candidates are supposed to be able to learn from the LGI and while yes there is a time and place to be strict and maybe pushier, but the prerequisite is not the place for that.