Downloading Dropbox to my older mac

You are correct, you do have the right to choose which operating system to use. That is completely your choice, and I will agree with you 100% on that. On the flip side, software companies have the choice of what operating systems they will fund their development staff to continue to write code for. If a newer operating system uses X version of API to support newer features and your previous generation operating system lacks X version of that API, the software vendor either has to A) cripple their software to not use that new version of API (if the new operating system will allow an older API to be used, which lots don't) or B) continue to pay their development staff to write and develop updates for a separate version of their software to work on just the older version of operating system you're running). Eventually, their "new" version and their "legacy" version will operate differently, adding confusion for the end users.

"Why can't my legacy version support files over 2GB?" Well, your computer from 1996 uses FAT32 file system, which physically can't handle a single file greater than 2GB. And the circle of entitlement for the latest and greatest features on antique systems continues. The end user has no idea what tech support is trying to explain. They just know they bought software that doesn't work like the version their friend bought and installed on a newer computer works. That's what happens when a software vendor maintains support for substantially older hardware/software platforms.

It's not the software vendor's fault that you want to use a technology that didn't exist in that time, but it'll be their problem when someone complains that they can't use it. From a business standpoint, it makes no sense to continue supporting a version of their software that will *not* run on new(er) computers. It's the same reason that your old version of Quattro that you ran on Windows 3.1 back in 1994 won't run on Windows 10. Microsoft, in their effort to support current technologies (both hardware and software) has to change the way their operating system works internally in order to provide that support. If we never had to advance and keep up with the times, computers would still be limited to 640KB of RAM and hard drives measured in megabytes, not gigabytes or terabytes.

Now, some vendors "push" the envelope much harder than they have to. Apple, for example, cuts off OS support for their hardware extremely prematurely in my opinion. The hardware from 3 years ago will still support the operating systems currently out (that's fact) but Apple will stop "allowing" your 3+ year old machine to recieve OSX updates. The inability to run a version of OSX on a previous generation of harsware is completely a manufacturer block to an extent. You can *technically* run OSX 10.12 (and even higher) on a 2007 iMac or Mac Pro. Apple prohibits this and will not let you do it as an "update", but with some very creative tinkering, people do it. However, it doesn't run all that great and requires installing additional drivers to make it work properly and Apple knows this, so they just block it altogether.

That said, Windows-based machines are much more flexible about what version of OS they will run. You can run Windows 10 on a Dell Optiplex 620 (released in 2005) as long as it has enough RAM and it runs well actually. Would I do it? No. Can it be done? Very easily. You bought an Apple though, and it's wirely known that they're are huge about pushing people to buy new hardware very quickly. They control the software, they control the hardware, they control the interoperability of the two. They profit all the way around. PCs are more open. Microsoft (for the most part) controls the OS, but there are dozens of manufacturers of hardware. The companies have to work together to some extent to provide support for eachother. 

Enough backstory I suppose. Your solution, as it sits now, is to go find another cloud storage company that will support whatever antique OS you're running (good luck with that by the way) or use the web interface, which requires installing nothing and will work on any OS that has a web browser new enough to at least load the dropbox.com website.