There is a significant difference between sarcasm meant to insult, and sarcasm meant to be playful humor with a point. Common uses of sarcasm include witty or playful language, humorous banter, the expression of frustration at unfortunate events, self-deprecation, and as a coping mechanism for difficult situations. I see that you couldn't tell the difference in that situation, but trust me, that person was not insulting you. They included themselves in the joke.
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There is a significant difference between sarcasm meant to insult, and sarcasm meant to be playful humor with a point. Common uses of sarcasm include witty or playful language, humorous banter, the expression of frustration at unfortunate events, self-deprecation, and as a coping mechanism for difficult situations. I see that you couldn't tell the difference in that situation, but trust me, that person was not insulting you. They included themselves in the joke.