There's no need to quote my message in full. This is a forum, not a newsgroup where messages can arrive out of order. Please only quote essential parts, not the full post.
Yes, the CPU will look at the cache first, but if the item it wan't isn't there then that's only a cache miss. Looking in the cache for something that isn't there doesn't count as a cache hit. Determining whether or not something is in cache needs to be done for every memory read so there doesn't seem any point including this in the count.
I honestly have no idea if write through caching writes to cache and memory simultaneously or sequentially. That will significantly affect the timing so I would have thought this would be an obvious thing to mention. I guess it could be implemented either way; it depends on the design.
The hit ratio is only relevant where a cache hit means no access to main memory is made. If you have write through caching then every memory write is also a cache write so the hit ratio is zero or 100% depending how you want to look at it, as previously explained.
Did the lecturers explain why they didn't agree? I think I listed all possibilities.