How do I look for pathogen in water with a microscope? Is it possible?
Yes your teacher is right. In a microscope you can see microorganisms. Now the question is to identify them as pathogens.

I guess what your teacher has in mind is to use specific culture mediums for different pathogens and see if anything is growing there, then you have a positive.

You could also do a PCR. This is extracting the DNA and amplify specific genes that you know belongs to pathogens.

But the most currently trendy analysis is metagenomics. Basically, you exctract the genetic material from the sample, then sequence and compare against public databases. This methodology allows the identification of everything that is there pathogens and non-pathogens.