I appreciate the sincerity of your question here and of your desire to contribute useful answers to EL&U. As you note in your comment to Hellion's answer the official EL&U guideline for casting a downvote is as follows:
Use your downvotes whenever you encounter an egregiously sloppy, no-effort-expended post, or an answer that is clearly and perhaps dangerously incorrect.
Your downvoted answer, it seems to me, isn't sloppy or clearly incorrect, and it shows a reasonable amount of effort (especially in coming up with additional examples of the form that the OP is asking about). Consequently, I can see why you might have been mystified by the initial downvote.
But there is a simple explanation for why downvotes happen in instances such as the one you bring up, and it is essentially the explanation that Dan Bron gives in a comment to Hellion's answer: People who have earned the privilege of downvoting use their own criteria for exercising that privilege. A vindictive pattern of downvoting a particular other user may lead to moderator intervention, but otherwise the downvoter isn't answerable to anyone.
Though I'm not a huge fan of downvoting, it arguably serves a quality-control function when applied by voters to signal "your answer doesn't show enough effort" or "your answer doesn't add anything meaningful to what other answers have already said" or even (perhaps) "your answer may be pretty good but it doesn't deserve the number of upvotes it has received, so I'm going to cancel one of them." I think that downvoting can be counterproductive when applied by voters to signal "I don't like your tone" or "I disagree with the result you reached even though your argument is reasonable" or "I don't think you should answer questions like this one because it only encourages more people to ask them."
But if you want to improve a downvoted answer or to avoid submitting future answers with similar shortcomings, what practical information does a downvote convey? How do you know which of the reasons listed above (or not listed here) triggered a downvote if no one explains the downvote?
The answer is, you can't know. Everyone who participates in EL&U—including some participants whose deep knowledge of language and usage leaves me in awe—receives downvotes from time to time. In the big picture it doesn't matter why they happen in a particular case, as long as you made a real effort to add something of value to the discussion.
You won't run afoul of the official standards for downvotes—egregious sloppiness, absence of effort, and obvious error—if you continue to answer questions at your current level. You'll probably incur fewer downvotes if, in addition, you avoid submitting answers that don't add anything substantially new to the answers that others have already submitted, and if (when possible) you bolster your position with citations to outside authorities.
Beyond that, as others here have noted, you just have to let it go. This site isn't a free-for-all; good answers generally receive respectful attention, and more votes up than down. If you stick with it long enough to develop a sense of what voters in general are looking for, you'll be able to make a consistently positive contribution to the site—and you'll be rewarded with (mostly) upvotes.