I don't...someone ignoring you doesn't automatically equal loneliness. It just means someone ignored you.
Loneliness is a feeling. Therefore unless you mean to say that the only time you feel lonely is when you get ignored, which doesn't make it the definition of loneliness at all IMO, more of a "reaction" to the "action" AKA the act of ignoring performed by other people, somewhat like saying that breaking bones is the definition of being in a car crash, because you can break bones in other situations as you can also feel lonely in other situations than when being ignored. At least it's possible for me.
qft. Also, I can be ignored without getting lonely. For instance, if I see someone I know at the grocery store, know they saw me, too, and they ignore me. Doesn't bother me at all. I'm not saying that being ignored can't result in being lonely. I'm just saying it doesn't always result in that.
Personally, I can think of atleast twenty people that could ignore me without me feeling lonely at all.
Thus proving my point. Now, being ignored by someone you really care about...I could see that leading to loneliness. However, I still wouldn't say that makes being ignored the definition of loneliness. The two have more of a cause and effect relationship, I think. Anyway, I'll stop quibbling about this now...
For the record, I can think of approximately 6 odd billions of human beings that can ignore me without me feeling anything at all, lonely included. "qft. Also, I can be ignored without getting lonely. For instance, if I see someone I know at the grocery store, know they saw me, too, and they ignore me. Doesn't bother me at all. I'm not saying that being ignored can't result in being lonely. I'm just saying it doesn't always result in that." Yes indeed, although I forgot to mention it that was another reason for me choosing the example that I did, car crashes doesn't necessarily equal broken bones either.