Assuming comes from the word, "assume". If you would cut up the word "assume" with some creativity, it makes "ass", "u" and "me". The saying "Assuming makes an ass out of you and me." is derived from that, and that itself can convey a message.
Socially, it can mean that assuming, generally speaking, may lead to misunderstanding, tension, and even conflict, as the party's thoughts/opinions/whatever may not be in the same pool.
In my interpretation, the message means to avoid assuming things as much as possible and look for details/clarification. This can apply to life decision making, since it's really true, like, you have an appointment with a friend of yours and you remember it was this week. However, you don't remember the day, but you assume it's on a weekend since you'd expect he/she would be free from work/school and thus you spend the Friday playing video games. But then, when you meet with your friend on Saturday, he/she seems pissed. It turns out the appointment was on the Friday you've spent playing video games.
Though you can't help but assume that a function is continuous if the situation forces you to assume that the function is continuous, since you can't perform any basic calculus required for it if it isn't a continuous function. That would fall under "in certain circumstances". IF X=Y, THEN Y=0. IF THIS IS THAT, THEN THAT IS THIS. TOUGH SHIT, MAN.
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