How to make a scatter plot using Apple Numbers?
Yes, it is possible to create a scatter chart in Numbers as you described.

However, sometimes creating a chart in Numbers turns out to be cumbersome for some reason in my experience as well, but, in this case, I could not replicate the problem you are describing. So I am unable to tell you what possibly the problem is in your case. 

In addition, I tried a few slightly different procedures, including the one described in this Apple support page, to create a scatter chart using the numbers you have given as an example and all turned out to be successful. I am attaching below the outcome of one of these trials.