if you're having trouble understanding counter words
I'm hardly an expert in the matter of Japanese counter words (the things that come in the course as "for counting birds", etc.), but I think the most useful comparison in English to wrap your head around them might be "garlic." We don't normally say "a garlic" or "two garlics." (My spellchecker is even signaling "garlics" as a typo, for example.) We say "a clove of garlic" or "five heads of garlic." In Japanese, it's just that all nouns are like "garlic."
Or look up "English terms of venery, by animal" on wikipedia, and you'll be amazed how hunters used different collective nouns for different animals.
In looking for these, I happened across the following blog post which describes the way in which animal counters in Japanese can be employed in playful ways: