Several of my earliest memories don't really have any significance to me either. I don't remember many of the funny or exciting events that occurred when I was young kid. i always found it strange that i can remember me playing with action figures but I don't remember any of my birthday parties!
My memories are actually the opposite. Every one that I have is of something important or if there was something exciting going on like a birthday party or going to Sea World.
I also find I remember more ordinary events than "special" events. I think for me, at least, this is because the majority of moments were ordinary, and so if a random event is to be remembered, it is more likely to be ordinary than special. Even if special events are more likely to be remembered, they would still have to be more likely than ordinary events are frequent to be the majority of early memories.
Perhaps for some people, special/emotional events get weighted much more heavily, and so they remember mostly special events, while for other people, most memories are of ordinary moments.
To add to the discussion, I've actually felt that most of my earliest memories were not "special events" as we think about them now - going to a great place, having a birthday, losing someone, etc - but were important in my mind and "special" because they feel like the first time for me in my memory. In my lab, I talk about a sensation that we experience on a normal basis, but it was special in my mind because I remembered it after all these years and something about the newness of a now-familiar experience makes it special to me.
My memories are opposite as well. Instead of them focusing on something important, exciting, or completely ordinary, they are all about the times I cried due to getting hurt, being upset, etc.
For such, our extremely aggresive dog bit my face when I was 5 (upper jaw in the eye and lower jaw in my cheek) and had to get stitches on said eyeball. The hilarious, albeit pathetic, part about it was the timing. My mother dressed me in a bunny costume since it was the day before Easter, so there I was at the hospital as a little white bunny soaked with blood.
My memory is different from yours in that there was a significant event that caused me to remember it. I think somehow this memory has some significance to you and that is why you remember it.