Because putty is smaller, faster, can work with serial ports too, which lets you use it to configure routers, debug arduinos, etc. It looks nicer, is easier to choose fonts, offers logging, offers easier clipboard control, and a lot of other features. In short, it's just a much more useful program.

PuTTY had a great VT100/xterm emulator long before any other free SSH option did. And it's a standalone app, no need for a giant Cygwin install.

Cygwin is a lot bigger and more time consuming to install. Putty is what? Half a meg and you're done? Much much much lower barrier to entry.

There's also the issue that in a corporate environment, having a much smaller attack surface is greatly preferred. Trying to get something like Cygwin past the security dept in a BIG company - quite challenging.

Because a lot of us don't need anything else Cygwin has to offer. So using it just to have OpenSSH feels like killing a house fly with a hammer.

PuTTY is also much quicker and easier to set up.

PuTTY is relatively portable, has just enough of a GUI to not require you use cmd.exe to run it, and is not GPL-ware.

(To be clear, I have nothing against the GPL, but some corporate environments avoid it like the plague.)

Cygwin/OpenSSH crashes/dies frequently (at least for me on Windows 7 / Cygwin64). Putty doesn't do that.

I use PuTTY at my job because we do all of our development on a Linux server but have Windows laptops issued to us.