Actually I'm not done. This kind of misinformation about ocean circulation is actually dangerous because it creates a misinformed idea of climate change. The effects of ocean warming are complex, and not everywhere is going to heat up universally, and you need to understand how thermohaline circulation affects your climate to get why.
Broadly speaking, global ocean currents are drawn by differences in temperature. Cold water sinks, warm water rises. This vertical movement translates to horizontal movement when you factor in latitude across the earth - equator warm, poles cold. So, when water cools down, it sinks, creating a void at the surface where warm water flows in. Similarly, when water warms up, it rises, creating a void at the bottom where cold water flows in. Boom, ocean currents. Here's a diagram from Encyclopedia Britannica to give you a general idea:
So here's how this affects climate. As an example, see the warm current that flows up through the Gulf of Mexico, across North America's eastern coast, and up towards Europe and the North Pole? This is one of the main reasons why the European continent isn't even colder than it already is. Water warms up in the Gulf of Mexico, experiencing lots of direct sunlight around the equator. At the same time, at the North Pole, water is cooling down, and sinking. The sinking water creates a void, causing the warm surface water to flow northward. Like the diagram shows, this also brings warm sea air, which affects the European climate. In short, the Gulf Stream keeps Europe from freezing over entirely.
So what happens when the oceans are heating up? In short, the temperature difference gets smaller. At the poles, if cold water is less cold, it sinks slower, meaning warm water doesn't flow in as strongly. As the ocean gets warmer, we lose that gradient from warm to cold, and these global currents grow weaker and weaker. If they're not flowing strong, they're not regulating land temperatures as efficiently.
In our earlier example, this would actually imply that Europe could get colder if the Gulf Stream weakens past a certain point. Without heat transported by the Gulf Stream, Europe could lose its natural air conditioning. (There is much discussion on this among climate scientists, which I am not, so take what I say with a grain of salt and do some reading from people smarter than I.) This is why "climate change" doesn't always look like progressively hotter days for everybody.
Why does it matter that you're informed about this? Because climate change deniers often like to point to the "complicated" effects of climate change, and go "see? if global warming was real, how come such-and-such is getting so much snow? checkmate, liberals." And if you thought all ocean water mostly stayed in one place and everything was nicely separated, you would have no context for why this is wrong. It's important to understand that such a huge global phenomenon like climate change is going to have a lot of widely varying effects. It's important to stay informed.
Uhhh tldr: water DOES move throughout the oceans and this is important for understanding the nuanced effects of climate change and combatting misinformation