I think a large part of it is that horizontal navigation as in OP is too thin, so if you do these natural dragging shapes your finger leaves the scrollable area. It may still work fine, but it feels wrong. Vertical scrolling on the other hand, because of what you say with our writing style, has a much larger grab area so we can easily stay within the box.
There's also parts specific to it being a menu: A vertically-aligned one usually has empty space on the right because the menu items probably aren't the same length, giving you a nice "grab area" (either your finger with touch or a place to put the mouse pointer for a scrollwheel) that doesn't hide anything. Plus scanning down a list is easier than sideways anyway because every item starts at the same place; just imagine how annoying it is to read a bulleted list on here when someone accidentally puts it all on one line because they didn't add an extra blank line between bullets.
Currently, it's also rare for webpages to feature horizontal scrolling, so by habit most users scroll vertically to access new information.
Discovery is also another reason mentioned by users elsewhere in these comments. Since horizontal scrolling is a rare behaviour, a clear signifier [0] is needed to quickly communicate that horizontal scrolling is a possibility, which is an extra problem that other potential methods don't have.
[0] https://sites.google.com/site/thedesignofeverydaythings/home...
Like it works just fine in mapping apps, which naturally align to a 2d canvas, but why does it feel so lousy to use with almost any other form of information?
Is it because we write left-to-right, top-to-bottom? So text chunks fit better with no horizontal scrolling? (I think this is also why vertical tabs are so much better than horizontal tabs).