Running is not necessarily a sport, it may be a hobby. If you run eg to catch up to someone, it's not a sport, just getting to a point quicker. It depends what you do it for, if it is for competitive reasons, then it may be a sport, but running is NOT a sport in general.
Sport- an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
Running clearly falls under that category. While running in a race a person is clearly using physical exertion and is a competition. Running was also the first sport in the Olypmics, so that certainly tells you it must be a sport.
I'll try to put it more clearly. Running is a sport because you using your body, and you are either competing with youself or others. Any type of running can technically be a sport because you are using your body to run.
Running is ONLY a sport if you are putting a comparison between you and others as a sort of contest. You're implying that if you run (like running across the road) it is immediately considered a sport. I believe this stands as one of your fatal flaws because you are not going in further depth 'why' you 'think' it's a sport. This is a point of clash in this debate and so far you are failing to affirmate the topic.
I believe my point shall stand because running is not always necessarily a sport but something we are not to compare with others, just a human characteristic that we use for many things, instinct of survival, to get to a point quicker etc, it's not mainly for competing.