Strength training.
I'm not really a professional, but I know quite a bit more about it than most, mainly by reading tons of books written by people who really know their shit.
Misconceptions:
"Strength training makes women big and bulky"
- Not possible for 99,99% of women without using steroids. Women lack the testosterone required to build big chunky muscles
"Strength training is not an important part of general physical fitness"
-This one seriously baffles me. A lot of people nowadays seem to think that physical fitness just means being able to jog for miles and miles. Bullshit. A wholly, completely fit human being is strong, fast, agile and has endurance, not just a frail little skeleton who's only ability is lumbering along at a slow speed for mile after mile. People seem to forget that we consist of more than just a brain and some organs; we have a musculo-skeletal system, and you need to keep that strong if you want to truly be physically fit. I can tell you from my own experience that a human being is quite simply happier strong than weak.
"Strength is not important for athletes"
-This one REALLY, REALLY baffles me. If strength is not important, why did baseball players suddenly start smashing home run records once they started roiding? To be fair, the majority of the people who claim that strength is not important for sports are recreational endurance athletes, like what most cyclists are. Obviously, strength is not a top priority for an endurance athletes, but to say that they don't benefit from it at all is complete horseshit. I'll paraphrase ol' Rips cyclist example. Each time a cyclist presses down on the pedal, they are using a portion of the maximum force that their leg (and posterior chain and so on) can produce. If the maximum force that their leg can produce goes up, that means that they use a smaller portion of that force to push down on the pedal. In other words, they become more effective at carrying their body across a distance. Strength is important to all sports, the only thing that varies is the cutoff point. Obviously, a cyclist is not going to need as much strength as, lets say, a wrestler.
"Strength training is dangerous and I'll get hurt"
-No. No it isn't. It is in fact significantly safer than, for example, running. In fact, strength specifically protects you from injury (stronger people are harder to kill etc.). Yeah, if you squat completely wrong, it could very well hurt you. That's the lesson: squat right. It will save you all kinds of trouble.
This last one isn't really a misconception as such, but it still kind of irritates me.
"I don't care about being able to squat 600 pounds"
- No one is saying that you need to squat 600 pounds, just that it would be be beneficial for you to be strong on a general level. People often equate strength with powerlifting or olympic weightlifting but those two sports are an extreme specialization in strength (or explosive strength in the case of OL, to be exact). I never try to convince anyone to do that, I just tell them that if you get stronger on a reasonable level, it will be beneficial.