Tyler Robinson 's classmate is speaking out in the aftermath of his arrest in connection with Charlie Kirk 's death ... sharing that the kid he remembers was a smart and goofy one, not a possible cold-hearted killer.

We caught up with the suspected shooter's classmate -- who chose to remain anonymous -- on "TMZ Live" Friday, mere hours after Robinson was apprehended and named as the main suspect in the fatal shooting of the conservative pundit. Gallery Launch Gallery

And, as the classmate told us, he found the news "extremely shocking," as he couldn't believe someone he went to middle school and high school with could possibly be culpable for this kind of violence.

Per the classmate, Robinson wasn't a loner at school by any means ... though, they did note that TR was "very onl

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