As a Geography nerd, it has been hard to remain restrained for this wrong.
First of all, we have to remember that the definition of continent is "big chunk of land." Problem is, this is not exactly clear, and there are loads of situations where the term is used very differently, including some fields of geography and geology.
Ms Sunnyfield in Kindergarten might have taught you that there were 7 continents. She also taught you that there were 9 planets and that you could see the Great Wall of China from the moon. This is because Ms Sunnyfield is a sociopathic liar, and should not be trusted.

That up there is what is usually meant by the Seven Continents. As you can see, most continents are either completely isolated from their neighbors or only share a narrow land border. For example, the border between North and South America is under 100 miles wide, the connection between Asia and Africa is not even 80 miles wide, and the border between Europe and Asia is about 1600 miles wide.
Yeah, 1600 miles. And it isn't even that tall a mountain range that stretches that length. The tallest mountain is shorter than a bunch of mountains in Indonesia, and we don't divide that into continents.