This is an interesting question because it happens to be a good analogy to some of the issues of time and space in quantum physics. But first let's cover the basics.
The simple past tense as referring to a completed event. The past continuous represents a continuing action and may be used to create a "scene" that is combined with other past continuous events or "interrupted" by a past simple event. The issue you are running into is a conflict between the time-semantics of the verb tense/aspect and the time-semantics of the sentence as a whole. Consider the following sentence, which is a typical use of the past continuous being interrupted with a simple past tense:
- I was watching a movie and cooking dinner when the phone rang.
Note that the "interruption" of the phone rang doesn't necessarily stop the other actions, but it does indicate a complete event that occurred. Now compare with the "interruption" using another past progressive:
- I was watching a movie and cooking dinner. Then the phone was ringing.
I had to use "then" to include an additional semantic constraint to force a sense of separation. But the action of the phone ringing just merges in with the other actions and leaves the reader/listener with an incomplete feeling. The reader/listener knows that there must be some conclusion to that ringing phone fairly soon. In the first of the above two sentences, one might follow with something like, "It was my best friend Margie" while in the second sentence one might follow with, "I debated whether or not to answer."
But the past tenses have limits in what they can meaningfully hold. What were you doing between 8 pm yesterday and 8 pm + 1 pico-second (1 billionth of a second) yesterday? You weren't really doing much of anything during that short time period, were you? You might have been in the process of beginning to focus your attention on some thought. And by the way, any thoughts you were in the process of having would have been 80 milliseconds in the past according to the latest research. It's simply too short of a time to think of doing anything that we typically think of as a meaningful activity. (Thus the quantum physics analogy.)
Similarly, what you were doing "when you were a child", without any other context, might be answered by writing a novel about your childhood. Or one could arbitrarily limit the scope to some parts of your childhood, or provide an equally broad answer like, "being a child" or "growing up". Or even more realistically, someone might say, "what you do mean? I was doing a lot of things when I was child."
So we think of our "doing things" as existing within certain limits of duration, beyond which it doesn't seem to make sense to talk about it anymore. In fact, the question of who "you" are -- both psychologically and even physically -- may begin to blur if you go back far-enough, expand time wide-enough, or narrow the duration to a small-enough time period.