At the very instant there were people who claimed it was assassination. If Oswald was on the TSBD steps he must have heard the sounds and saw the commotion, people running towards Grassy knoll. If you were there, what would you think that is happening? Firecrackers, motorcycle backfires or gun shots? People reactions corresponds to what? Nah, it was firecrackers guys, clam down and go home... Nah, it was back fire... Or, it were gun shots and people got panic? Immediate reaction of everybody could only mean that there were gun shots and there was no reason Oswald to think about anything else but gun shots.
Why he did not stay? Well, he got panicked as everybody else.
If he was on the steps of the TSBD then he was surrounded by people, by his fellow co-workers like Frazier and others. They can give him an alibi. There's no need to take off. But I thought you believed he was inside having lunch? He said in a brief interview that he was inside the building at the time of the shooting.
Again: the people who were there, around the steps, didn't know exactly what happened. It was chaos and confusion. Nobody knew what happened. Those who were there said they asked each other about what was going on. In fact, a number of people ran to the Grassy Knoll, fence and overpass. That's where some people thought the shots came from.
Oswald did numerous things after the shooting that I simply don't think an innocent person would have done. In fact, he did things that a guilty person would do. But others, like you, obviously disagree.
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