I like Dog = ドッグという人が好き・「ドッグ」というものが好き （例えば、「ドッグ」というブランドのビール）
I love hamburgers = ハンバーグが大好き
I love Hamburger = ハンバーガーという人が大好き・ハンバーガーというものが大好き （例えば、「ハンバーガー」という名前の付いているパチンコ屋）
You may also like to mention that what is most commonly referred to as the "plural" form（複数形）of nouns in English is actually the "non-singular" form（非単数形）.
This is why you have to say "I don't have any cats" or "I have zero cats" instead of, "I don't have any cat" and "I have zero cat".
The form "cat" is only used when talking about exactly one cat, in every other case it must be "cats". I really don't know why they teach the singular form first. I think this causes a great deal of confusion.
You wanted to say "General statements in English use the plural noun form."
You came up with:
I would suggest:
I cannot guarantee this is correct, but here's why I'd suggest this:
"statement" is a word with many meanings. 発言 means an "utterance" and in that sense reflects a statement. In this context, statement is a technical word for philosophy that refers to how we express a proposition. E.g., "dogs are cute." As such, the meaning that you're closest to sounds like a 命題 which is the Japanese word for this sort of thing in philosophy.
"general". General is a word with definitions that can't all be used interchangeable. One definition is affecting or concerning all or most people or things (from google). Another is "not limited"; another is "inexact." I think what you're meaning in your sentence based on context is that we make universal claims in this way. So I'd suggest 普遍 over 一般, because I take 一般 to mean general in the sense of a "normal" or "common."
I switched it to the ている for rather plain verb form because if memory serves me correctly that's going to better capture a linguistic practice whereas a 使う fits better with single instances of use.
Anyway, we'll see if these suggestions are upvoted or downvoted.