never thought about it being an american thing

So, two things about culture:

First, 90% of human culture is below awareness or subconscious - nobody ever teaches it to you, you don't think about doing it. 

But second, culture is part of the human adaptation to nature - instead of evolving claws to hunt and fur to survive winter, we developed tools to make clothes and language to teach our children how to use them. 

How you move through and use physical space is typically not consciously taught, it's the part of the culture you learn naturally by observing others. 

One example is personal space - we've all heard of the concept, but I bet you can't point to the ground and show me where your personal space ends - you just know when someone's too close or too far away.

Americans are notorious for having a huge personal space and that's reflected in how we design spaces - our bedrooms have doors that close and lock - we have easy chairs in our living room so everyone has their own seat - we set aside individual spaces for different activities - we don't eat dinner on our bedroom floor; the washing machine goes in its own laundry room, and we don't hang clothes to dry in the kitchen.

Spend time overseas, and you'll immediately begin to feel the difference - here in Japan, apartments often have sliding doors with no latch, and rooms are all combined use - a typical apartment is an LDK, a combined living room/dining room/kitchen - you cook, eat, and watch TV in the same room; on rainy days you dry your clothes in the LDK, and the washer (no room for a drier) is in your bathroom.

Try this: Google up a picture of a British apartment and check how weird you feel seeing a washing machine in the kitchen.

Culture is part of our adaptation to nature, so it frequently replaces our natural behaviors - so a lot of people mistake the unconscious parts of their culture as universal human nature - like, hey, doesn't everyone lean? 

Well, no, and it's part of how we utilize space - Americans like to segment space - this room is for this, that room is for that - and we hate nothing more than people cluttering, blocking, or taking up space - it's one of the ways we insult each other - "Look at this waste of space!"

When there's no walls or doors to segment space, our cultural instinct is to move aside, get out of the way - what's the best way to do that? Find a wall or a pillar and lean against it. Get out of the way, get out of the flow of traffic. And don't just stand there, plant yourself - communicate to the people around you that you aren't moving anywhere - don't mind me, don't try to dodge me, I'm stuck to this wall. 

But, again, this is all unconscious - you don't notice or think about these rules until someone breaks them. A HUGE culture shock for Americans here in Japan is just how much people get in your way, or jump out in front of you, or rub against you on overcrowded trains.

Those are all ways to start a fight in the US, so you immediately get an understanding of why it's called culture shock and why people talk about it like an illness - your brain is constantly telling you this guy wants to fight you, but it's literally just a little girl who fell asleep with her head on your shoulder. It's stressful, and you have to consciously manage your unconscious reflexes. 

Anyway, tldr, Americans lean because we value other people's space and want to get out of the way.