What's the call runner on first base and second base with no outs. Fly ball hit to deep Outfield runner on first base runs to second but does not touch. Sees ball caught and returns to first base. Defense appeals runner and is called out. Umpire explanation is because runner turned around base obligated to touch base upon return to first base.. Doesn't matter that base was not touched initially.

youngen ... We answered this for you previously but, unfortunately, the thread became polluted by unrelated personal insult commentary and had to be removed ... Here's your answer again ...

Once your base runner has passed second base, he is presumed to have legally acquired that base unless/until there is a subsequent appeal to the contrary ... With that presumption of having legally acquired the base comes a related obligation to (re-)touch it when retreating back the other way to first base ... The umpire's out call on appeal was correct for the failure to touch 2B on the way back to 1B during the play as described ... Thanks for writing (twice) ...

I and many other colleagues of mine use the term 'last time' by because on the last time the runner passes his base he must complete his obligation to touching the base. Nothing fancy.

Youngen, Dave is correct in his explanation.
You said runner on first runs to second but does not touch. I presume he didn’t tag up.
If he passed second and was on his way to third the umpire made the correct call!!