"You're either good at art or science, never both unless you're a mad scientist".
Yet I find myself looking towards science now and then when attempting to improve my art. Especially anatomy for drawing character designs. When writing I often have to look up small technical details to make sure that a scene actually works.
Also, my family seems to consist of individuals that excel in both art and science. I know a good portion of friends that do as well.
To a certain extent, I understand where that teacher was coming from. When dealing with realistic styles, sometimes it can be tempting to include too much detail (often in an unflattering way) which can ruin the piece. However, having a technical knowledge of certain things can come in handy when creating art.
If my friend didn't know so much about the inner workings of old planes, he wouldn't be able to draw them so accurately and picturesque.
Not too long ago I saw a film where two parents raised this kid who was destined to be a scientist, and pressured him to become an artist instead in order to see how much influence nature has over nurture. The problem with this premise is that it works under the assumption that the two are automatically incompatible. That a proper scientist is therefore incapable of being creative. However, this is simply not the case. Some scientists struggle with this, others don't.
Is it more common/ likely for scientific types to have difficulty with comprehending impractical thinking, unorthodox solutions, and art? Where did this stereotype/cliché come from? Am I surrounded by genius mad scientists?

That quote should only worry you if you see being a mad scientist as a bad thing.
(and yes, I am taking it as a compliment. muhahaha...)